Daily Papers

Reinforcement Learning with Verifiable Rewards (RLVR) is a powerful paradigm for enhancing the reasoning ability of Large Language Models (LLMs). Yet current RLVR methods often explore poorly, leading to premature convergence and entropy collapse. To address this challenge, we introduce Curiosity-Driven Exploration (CDE), a framework that leverages the model's own intrinsic sense of curiosity to guide exploration. We formalize curiosity with signals from both the actor and the critic: for the actor, we use perplexity over its generated response, and for the critic, we use the variance of value estimates from a multi-head architecture. Both signals serve as an exploration bonus within the RLVR framework to guide the model. Our theoretical analysis shows that the actor-wise bonus inherently penalizes overconfident errors and promotes diversity among correct responses; moreover, we connect the critic-wise bonus to the well-established count-based exploration bonus in RL. Empirically, our method achieves an approximate +3 point improvement over standard RLVR using GRPO/PPO on AIME benchmarks. Further analysis identifies a calibration collapse mechanism within RLVR, shedding light on common LLM failure modes.

Exploration bonuses in reinforcement learning guide long-horizon exploration by defining custom intrinsic objectives. Several exploration objectives like count-based bonuses, pseudo-counts, and state-entropy maximization are non-stationary and hence are difficult to optimize for the agent. While this issue is generally known, it is usually omitted and solutions remain under-explored. The key contribution of our work lies in transforming the original non-stationary rewards into stationary rewards through an augmented state representation. For this purpose, we introduce the Stationary Objectives For Exploration (SOFE) framework. SOFE requires identifying sufficient statistics for different exploration bonuses and finding an efficient encoding of these statistics to use as input to a deep network. SOFE is based on proposing state augmentations that expand the state space but hold the promise of simplifying the optimization of the agent's objective. We show that SOFE improves the performance of several exploration objectives, including count-based bonuses, pseudo-counts, and state-entropy maximization. Moreover, SOFE outperforms prior methods that attempt to stabilize the optimization of intrinsic objectives. We demonstrate the efficacy of SOFE in hard-exploration problems, including sparse-reward tasks, pixel-based observations, 3D navigation, and procedurally generated environments.

We propose a new method for count-based exploration in high-dimensional state spaces. Unlike previous work which relies on density models, we show that counts can be derived by averaging samples from the Rademacher distribution (or coin flips). This insight is used to set up a simple supervised learning objective which, when optimized, yields a state's visitation count. We show that our method is significantly more effective at deducing ground-truth visitation counts than previous work; when used as an exploration bonus for a model-free reinforcement learning algorithm, it outperforms existing approaches on most of 9 challenging exploration tasks, including the Atari game Montezuma's Revenge.

Exploration remains a critical challenge in online reinforcement learning, as an agent must effectively explore unknown environments to achieve high returns. Currently, the main exploration algorithms are primarily count-based methods and curiosity-based methods, with prediction-error methods being a prominent example. In this paper, we propose a novel method called Random Distribution Distillation (RDD), which samples the output of a target network from a normal distribution. RDD facilitates a more extensive exploration by explicitly treating the difference between the prediction network and the target network as an intrinsic reward. Furthermore, by introducing randomness into the output of the target network for a given state and modeling it as a sample from a normal distribution, intrinsic rewards are bounded by two key components: a pseudo-count term ensuring proper exploration decay and a discrepancy term accounting for predictor convergence. We demonstrate that RDD effectively unifies both count-based and prediction-error approaches. It retains the advantages of prediction-error methods in high-dimensional spaces, while also implementing an intrinsic reward decay mode akin to the pseudo-count method. In the experimental section, RDD is compared with more advanced methods in a series of environments. Both theoretical analysis and experimental results confirm the effectiveness of our approach in improving online exploration for reinforcement learning tasks.

Realistic environments often provide agents with very limited feedback. When the environment is initially unknown, the feedback, in the beginning, can be completely absent, and the agents may first choose to devote all their effort on exploring efficiently. The exploration remains a challenge while it has been addressed with many hand-tuned heuristics with different levels of generality on one side, and a few theoretically-backed exploration strategies on the other. Many of them are incarnated by intrinsic motivation and in particular explorations bonuses. A common rule of thumb for exploration bonuses is to use 1/n bonus that is added to the empirical estimates of the reward, where n is a number of times this particular state (or a state-action pair) was visited. We show that, surprisingly, for a pure-exploration objective of reward-free exploration, bonuses that scale with 1/n bring faster learning rates, improving the known upper bounds with respect to the dependence on the horizon H. Furthermore, we show that with an improved analysis of the stopping time, we can improve by a factor H the sample complexity in the best-policy identification setting, which is another pure-exploration objective, where the environment provides rewards but the agent is not penalized for its behavior during the exploration phase.

Achieving effective test-time scaling requires models to engage in In-Context Exploration -- the intrinsic ability to generate, verify, and refine multiple reasoning hypotheses within a single continuous context. Grounded in State Coverage theory, our analysis identifies a critical bottleneck to enabling this capability: while broader state coverage requires longer reasoning trajectories, the probability of sampling such sequences decays exponentially during autoregressive generation, a phenomenon we term the ``Shallow Exploration Trap''. To bridge this gap, we propose Length-Incentivized Exploration(\method). This simple yet effective recipe explicitly encourages models to explore more via a length-based reward coupled with a redundancy penalty, thereby maximizing state coverage in two-step manner. Comprehensive experiments across different models (Qwen3, Llama) demonstrate that \method effectively incentivize in-context exploration. As a result, our method achieves an average improvement of 4.4\% on in-domain tasks and a 2.7\% gain on out-of-domain benchmarks.

Reinforcement learning (RL) has emerged as a powerful method for improving the reasoning abilities of large language models (LLMs). Outcome-based RL, which rewards policies solely for the correctness of the final answer, yields substantial accuracy gains but also induces a systematic loss in generation diversity. This collapse undermines real-world performance, where diversity is critical for test-time scaling. We analyze this phenomenon by viewing RL post-training as a sampling process and show that, strikingly, RL can reduce effective diversity even on the training set relative to the base model. Our study highlights two central findings: (i) a transfer of diversity degradation, where reduced diversity on solved problems propagates to unsolved ones, and (ii) the tractability of the outcome space, since reasoning tasks admit only a limited set of distinct answers. Motivated by these insights, we propose outcome-based exploration, which assigns exploration bonuses according to final outcomes. We introduce two complementary algorithms: historical exploration, which encourages rarely observed answers via UCB-style bonuses, and batch exploration, which penalizes within-batch repetition to promote test-time diversity. Experiments on standard competition math with Llama and Qwen models demonstrate that both methods improve accuracy while mitigating diversity collapse. On the theoretical side, we formalize the benefit of outcome-based exploration through a new model of outcome-based bandits. Together, these contributions chart a practical path toward RL methods that enhance reasoning without sacrificing the diversity essential for scalable deployment.

Exploration in environments which differ across episodes has received increasing attention in recent years. Current methods use some combination of global novelty bonuses, computed using the agent's entire training experience, and episodic novelty bonuses, computed using only experience from the current episode. However, the use of these two types of bonuses has been ad-hoc and poorly understood. In this work, we shed light on the behavior of these two types of bonuses through controlled experiments on easily interpretable tasks as well as challenging pixel-based settings. We find that the two types of bonuses succeed in different settings, with episodic bonuses being most effective when there is little shared structure across episodes and global bonuses being effective when more structure is shared. We develop a conceptual framework which makes this notion of shared structure precise by considering the variance of the value function across contexts, and which provides a unifying explanation of our empirical results. We furthermore find that combining the two bonuses can lead to more robust performance across different degrees of shared structure, and investigate different algorithmic choices for defining and combining global and episodic bonuses based on function approximation. This results in an algorithm which sets a new state of the art across 16 tasks from the MiniHack suite used in prior work, and also performs robustly on Habitat and Montezuma's Revenge.

Curiosity-based reward schemes can present powerful exploration mechanisms which facilitate the discovery of solutions for complex, sparse or long-horizon tasks. However, as the agent learns to reach previously unexplored spaces and the objective adapts to reward new areas, many behaviours emerge only to disappear due to being overwritten by the constantly shifting objective. We argue that merely using curiosity for fast environment exploration or as a bonus reward for a specific task does not harness the full potential of this technique and misses useful skills. Instead, we propose to shift the focus towards retaining the behaviours which emerge during curiosity-based learning. We posit that these self-discovered behaviours serve as valuable skills in an agent's repertoire to solve related tasks. Our experiments demonstrate the continuous shift in behaviour throughout training and the benefits of a simple policy snapshot method to reuse discovered behaviour for transfer tasks.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a crucial paradigm for incentivizing reasoning capabilities in Large Language Models (LLMs). Due to vast state-action spaces and reward sparsity in reasoning tasks, existing methods often struggle with deficient exploration and poor sample efficiency. In the paper, we propose DIVER (Diversity-Incentivized Exploration for VersatilE Reasoning), an innovative framework that highlights the pivotal role of global sequence-level diversity to incentivize deep exploration for versatile reasoning. We first conduct a primary empirical study to reveal a strong positive correlation between global diversity and reasoning capacity. Building on this insight, we introduce global diversity incentives as an intrinsic reward to promote deep exploration in a semantically structured space. Incorporating the intrinsic reward, we develop a potential-based reward shaping mechanism to preserve optimal policy invariance and design simple heuristics to mitigate possible reward hacking. Experimental results show that DIVER outperforms competitive RLVR baselines with various exploration strategies on both in-domain and out-of-domain tasks, excelling in both Pass@1 and Pass@k evaluations. Our code is available at https://github.com/NJU-RL/DIVER.

Reinforcement learning (RL) promises to expand the capabilities of language models, but it is unclear if current RL techniques promote the discovery of novel behaviors, or simply sharpen those already present in the base model. In this paper, we investigate the value of deliberate exploration -- explicitly incentivizing the model to discover novel and diverse behaviors -- and aim to understand how the knowledge in pre-trained models can guide this search. Our main finding is that exploration with a simple, principled, representation-based bonus derived from the pre-trained language model's hidden states significantly improves diversity and pass@k rates -- both for post-training, and in a novel inference-time scaling setting we introduce. For inference-time, exploration with representation-based diversity improves efficiency, consistently improving pass@k rates across a variety of models and reasoning tasks. For example, for Qwen-2.5-14b-Instruct we obtain over 50% improvement in verifier efficiency on almost all tasks. For post-training, we show that integrating this exploration strategy into an RL pipeline improves reasoning performance over that of the initial model and over standard RL post-training. For example, on AIME 2024, our post-trained Qwen-2.5-7b-Instruct's pass@80 matches the pass@256 of GRPO on the same model, demonstrating a 3x improvement in test-time sample efficiency. Overall, our findings suggest that deliberate exploration -- with the right notion of diversity -- is a practical path toward discovery of new behaviors beyond sharpening.

We introduce an exploration bonus for deep reinforcement learning methods that is easy to implement and adds minimal overhead to the computation performed. The bonus is the error of a neural network predicting features of the observations given by a fixed randomly initialized neural network. We also introduce a method to flexibly combine intrinsic and extrinsic rewards. We find that the random network distillation (RND) bonus combined with this increased flexibility enables significant progress on several hard exploration Atari games. In particular we establish state of the art performance on Montezuma's Revenge, a game famously difficult for deep reinforcement learning methods. To the best of our knowledge, this is the first method that achieves better than average human performance on this game without using demonstrations or having access to the underlying state of the game, and occasionally completes the first level.

Ensuring sufficient exploration is a central challenge when training meta-reinforcement learning (meta-RL) agents to solve novel environments. Conventional solutions to the exploration-exploitation dilemma inject explicit incentives such as randomization, uncertainty bonuses, or intrinsic rewards to encourage exploration. In this work, we hypothesize that an agent trained solely to maximize a greedy (exploitation-only) objective can nonetheless exhibit emergent exploratory behavior, provided three conditions are met: (1) Recurring Environmental Structure, where the environment features repeatable regularities that allow past experience to inform future choices; (2) Agent Memory, enabling the agent to retain and utilize historical interaction data; and (3) Long-Horizon Credit Assignment, where learning propagates returns over a time frame sufficient for the delayed benefits of exploration to inform current decisions. Through experiments in stochastic multi-armed bandits and temporally extended gridworlds, we observe that, when both structure and memory are present, a policy trained on a strictly greedy objective exhibits information-seeking exploratory behavior. We further demonstrate, through controlled ablations, that emergent exploration vanishes if either environmental structure or agent memory is absent (Conditions 1 & 2). Surprisingly, removing long-horizon credit assignment (Condition 3) does not always prevent emergent exploration-a result we attribute to the pseudo-Thompson Sampling effect. These findings suggest that, under the right prerequisites, exploration and exploitation need not be treated as orthogonal objectives but can emerge from a unified reward-maximization process.

Intrinsic reward shaping has emerged as a prevalent approach to solving hard-exploration and sparse-rewards environments in reinforcement learning (RL). While single intrinsic rewards, such as curiosity-driven or novelty-based methods, have shown effectiveness, they often limit the diversity and efficiency of exploration. Moreover, the potential and principle of combining multiple intrinsic rewards remains insufficiently explored. To address this gap, we introduce HIRE (Hybrid Intrinsic REward), a flexible and elegant framework for creating hybrid intrinsic rewards through deliberate fusion strategies. With HIRE, we conduct a systematic analysis of the application of hybrid intrinsic rewards in both general and unsupervised RL across multiple benchmarks. Extensive experiments demonstrate that HIRE can significantly enhance exploration efficiency and diversity, as well as skill acquisition in complex and dynamic settings.

Exploration remains a critical issue in deep reinforcement learning for an agent to attain high returns in unknown environments. Although the prevailing exploration Random Network Distillation (RND) algorithm has been demonstrated to be effective in numerous environments, it often needs more discriminative power in bonus allocation. This paper highlights the "bonus inconsistency" issue within RND, pinpointing its primary limitation. To address this issue, we introduce the Distributional RND (DRND), a derivative of the RND. DRND enhances the exploration process by distilling a distribution of random networks and implicitly incorporating pseudo counts to improve the precision of bonus allocation. This refinement encourages agents to engage in more extensive exploration. Our method effectively mitigates the inconsistency issue without introducing significant computational overhead. Both theoretical analysis and experimental results demonstrate the superiority of our approach over the original RND algorithm. Our method excels in challenging online exploration scenarios and effectively serves as an anti-exploration mechanism in D4RL offline tasks. Our code is publicly available at https://github.com/yk7333/DRND.

Exploration in sparse reward environments remains one of the key challenges of model-free reinforcement learning. Instead of solely relying on extrinsic rewards provided by the environment, many state-of-the-art methods use intrinsic rewards to encourage exploration. However, we show that existing methods fall short in procedurally-generated environments where an agent is unlikely to visit a state more than once. We propose a novel type of intrinsic reward which encourages the agent to take actions that lead to significant changes in its learned state representation. We evaluate our method on multiple challenging procedurally-generated tasks in MiniGrid, as well as on tasks with high-dimensional observations used in prior work. Our experiments demonstrate that this approach is more sample efficient than existing exploration methods, particularly for procedurally-generated MiniGrid environments. Furthermore, we analyze the learned behavior as well as the intrinsic reward received by our agent. In contrast to previous approaches, our intrinsic reward does not diminish during the course of training and it rewards the agent substantially more for interacting with objects that it can control.

In the Reinforcement Learning (RL) framework, the learning is guided through a reward signal. This means that in situations of sparse rewards the agent has to focus on exploration, in order to discover which action, or set of actions leads to the reward. RL agents usually struggle with this. Exploration is the focus of Quality-Diversity (QD) methods. In this thesis, we approach the problem of sparse rewards with these algorithms, and in particular with Novelty Search (NS). This is a method that only focuses on the diversity of the possible policies behaviors. The first part of the thesis focuses on learning a representation of the space in which the diversity of the policies is evaluated. In this regard, we propose the TAXONS algorithm, a method that learns a low-dimensional representation of the search space through an AutoEncoder. While effective, TAXONS still requires information on when to capture the observation used to learn said space. For this, we study multiple ways, and in particular the signature transform, to encode information about the whole trajectory of observations. The thesis continues with the introduction of the SERENE algorithm, a method that can efficiently focus on the interesting parts of the search space. This method separates the exploration of the search space from the exploitation of the reward through a two-alternating-steps approach. The exploration is performed through NS. Any discovered reward is then locally exploited through emitters. The third and final contribution combines TAXONS and SERENE into a single approach: STAX. Throughout this thesis, we introduce methods that lower the amount of prior information needed in sparse rewards settings. These contributions are a promising step towards the development of methods that can autonomously explore and find high-performance policies in a variety of sparse rewards settings.

A grand challenge in reinforcement learning is intelligent exploration, especially when rewards are sparse or deceptive. Two Atari games serve as benchmarks for such hard-exploration domains: Montezuma's Revenge and Pitfall. On both games, current RL algorithms perform poorly, even those with intrinsic motivation, which is the dominant method to improve performance on hard-exploration domains. To address this shortfall, we introduce a new algorithm called Go-Explore. It exploits the following principles: (1) remember previously visited states, (2) first return to a promising state (without exploration), then explore from it, and (3) solve simulated environments through any available means (including by introducing determinism), then robustify via imitation learning. The combined effect of these principles is a dramatic performance improvement on hard-exploration problems. On Montezuma's Revenge, Go-Explore scores a mean of over 43k points, almost 4 times the previous state of the art. Go-Explore can also harness human-provided domain knowledge and, when augmented with it, scores a mean of over 650k points on Montezuma's Revenge. Its max performance of nearly 18 million surpasses the human world record, meeting even the strictest definition of "superhuman" performance. On Pitfall, Go-Explore with domain knowledge is the first algorithm to score above zero. Its mean score of almost 60k points exceeds expert human performance. Because Go-Explore produces high-performing demonstrations automatically and cheaply, it also outperforms imitation learning work where humans provide solution demonstrations. Go-Explore opens up many new research directions into improving it and weaving its insights into current RL algorithms. It may also enable progress on previously unsolvable hard-exploration problems in many domains, especially those that harness a simulator during training (e.g. robotics).

Exploration is a key problem in reinforcement learning, since agents can only learn from data they acquire in the environment. With that in mind, maintaining a population of agents is an attractive method, as it allows data be collected with a diverse set of behaviors. This behavioral diversity is often boosted via multi-objective loss functions. However, those approaches typically leverage mean field updates based on pairwise distances, which makes them susceptible to cycling behaviors and increased redundancy. In addition, explicitly boosting diversity often has a detrimental impact on optimizing already fruitful behaviors for rewards. As such, the reward-diversity trade off typically relies on heuristics. Finally, such methods require behavioral representations, often handcrafted and domain specific. In this paper, we introduce an approach to optimize all members of a population simultaneously. Rather than using pairwise distance, we measure the volume of the entire population in a behavioral manifold, defined by task-agnostic behavioral embeddings. In addition, our algorithm Diversity via Determinants (DvD), adapts the degree of diversity during training using online learning techniques. We introduce both evolutionary and gradient-based instantiations of DvD and show they effectively improve exploration without reducing performance when better exploration is not required.

The rapid progress of large language models (LLMs) has sparked growing interest in building Artificial General Intelligence (AGI) within Graphical User Interface (GUI) environments. However, existing GUI agents based on LLMs or vision-language models (VLMs) often fail to generalize to novel environments and rely heavily on manually curated, diverse datasets. To overcome these limitations, we introduce ScreenExplorer, a VLM trained via Group Relative Policy Optimization(GRPO) in real, dynamic, and open-ended GUI environments. Innovatively, we introduced a world-model-based curiosity reward function to help the agent overcome the cold-start phase of exploration. Additionally, distilling experience streams further enhances the model's exploration capabilities. Our training framework enhances model exploration in open GUI environments, with trained models showing better environmental adaptation and sustained exploration compared to static deployment models. Our findings offer a scalable pathway toward AGI systems with self-improving capabilities in complex interactive settings.

A prevailing view in Reinforcement Learning for Verifiable Rewards (RLVR) interprets recent progress through the lens of an exploration-exploitation trade-off, a perspective largely shaped by token-level metrics. We re-examine this perspective, proposing that this perceived trade-off may not be a fundamental constraint but rather an artifact of the measurement level. To investigate this, we shift the analysis to the semantically rich hidden-state space, adopting Effective Rank (ER) to quantify exploration and proposing its novel first- and second-order derivatives, named Effective Rank Velocity (ERV) and Effective Rank Acceleration (ERA), to capture exploitation dynamics. Our analysis reveals that at the hidden-state level, exploration and exploitation could be decoupled (Sec. 4). This finding reveals an opportunity to enhance both capacities simultaneously. This insight motivates our method, Velocity-Exploiting Rank-Learning (VERL), the first to operationalize the principle of synergistic exploration-exploitation enhancement by directly shaping the RL advantage function. The key innovation is leveraging the theoretically stable ERA as a predictive meta-controller to create a synergistic, dual-channel incentive structure. Instead of forcing a trade-off, VERL prospectively amplifies rewards for exploration to preempt overconfidence and reinforces exploitative gains to consolidate reasoning. Experiments across diverse LLMs and reasoning benchmarks show consistent gains, including up to 21.4% absolute accuracy improvement on the challenging Gaokao 2024 dataset.

Large language model based agents often fail in unfamiliar environments due to premature exploitation: a tendency to act on prior knowledge before acquiring sufficient environment-specific information. We identify autonomous exploration as a critical yet underexplored capability for building adaptive agents. To formalize and quantify this capability, we introduce Exploration Checkpoint Coverage, a verifiable metric that measures how broadly an agent discovers key states, objects, and affordances. Our systematic evaluation reveals that agents trained with standard task-oriented reinforcement learning consistently exhibit narrow and repetitive behaviors that impede downstream performance. To address this limitation, we develop a training strategy that interleaves task-execution rollouts and exploration rollouts, with each type of rollout optimized by its corresponding verifiable reward. Building on this training strategy, we propose the Explore-then-Act paradigm, which decouples information-gathering from task execution: agents first utilize an interaction budget to acquire grounded environmental knowledge, then leverage it for task resolution. Our results demonstrate that learning to systematically explore is imperative for building generalizable and real-world-ready agents.

Reinforcement learning algorithms typically struggle in the absence of a dense, well-shaped reward function. Intrinsically motivated exploration methods address this limitation by rewarding agents for visiting novel states or transitions, but these methods offer limited benefits in large environments where most discovered novelty is irrelevant for downstream tasks. We describe a method that uses background knowledge from text corpora to shape exploration. This method, called ELLM (Exploring with LLMs) rewards an agent for achieving goals suggested by a language model prompted with a description of the agent's current state. By leveraging large-scale language model pretraining, ELLM guides agents toward human-meaningful and plausibly useful behaviors without requiring a human in the loop. We evaluate ELLM in the Crafter game environment and the Housekeep robotic simulator, showing that ELLM-trained agents have better coverage of common-sense behaviors during pretraining and usually match or improve performance on a range of downstream tasks.

In many real-world scenarios, rewards extrinsic to the agent are extremely sparse, or absent altogether. In such cases, curiosity can serve as an intrinsic reward signal to enable the agent to explore its environment and learn skills that might be useful later in its life. We formulate curiosity as the error in an agent's ability to predict the consequence of its own actions in a visual feature space learned by a self-supervised inverse dynamics model. Our formulation scales to high-dimensional continuous state spaces like images, bypasses the difficulties of directly predicting pixels, and, critically, ignores the aspects of the environment that cannot affect the agent. The proposed approach is evaluated in two environments: VizDoom and Super Mario Bros. Three broad settings are investigated: 1) sparse extrinsic reward, where curiosity allows for far fewer interactions with the environment to reach the goal; 2) exploration with no extrinsic reward, where curiosity pushes the agent to explore more efficiently; and 3) generalization to unseen scenarios (e.g. new levels of the same game) where the knowledge gained from earlier experience helps the agent explore new places much faster than starting from scratch. Demo video and code available at https://pathak22.github.io/noreward-rl/

Robots in many real-world settings have access to force/torque sensors in their gripper and tactile sensing is often necessary in tasks that involve contact-rich motion. In this work, we leverage surprise from mismatches in touch feedback to guide exploration in hard sparse-reward reinforcement learning tasks. Our approach, Touch-based Curiosity (ToC), learns what visible objects interactions are supposed to "feel" like. We encourage exploration by rewarding interactions where the expectation and the experience don't match. In our proposed method, an initial task-independent exploration phase is followed by an on-task learning phase, in which the original interactions are relabeled with on-task rewards. We test our approach on a range of touch-intensive robot arm tasks (e.g. pushing objects, opening doors), which we also release as part of this work. Across multiple experiments in a simulated setting, we demonstrate that our method is able to learn these difficult tasks through sparse reward and curiosity alone. We compare our cross-modal approach to single-modality (touch- or vision-only) approaches as well as other curiosity-based methods and find that our method performs better and is more sample-efficient.

Recommending novel content, which expands user horizons by introducing them to new interests, has been shown to improve users' long-term experience on recommendation platforms chen2021values. Users however are not constantly looking to explore novel content. It is therefore crucial to understand their novelty-seeking intent and adjust the recommendation policy accordingly. Most existing literature models a user's propensity to choose novel content or to prefer a more diverse set of recommendations at individual interactions. Hierarchical structure, on the other hand, exists in a user's novelty-seeking intent, which is manifested as a static and intrinsic user preference for seeking novelty along with a dynamic session-based propensity. To this end, we propose a novel hierarchical reinforcement learning-based method to model the hierarchical user novelty-seeking intent, and to adapt the recommendation policy accordingly based on the extracted user novelty-seeking propensity. We further incorporate diversity and novelty-related measurement in the reward function of the hierarchical RL (HRL) agent to encourage user exploration chen2021values. We demonstrate the benefits of explicitly modeling hierarchical user novelty-seeking intent in recommendations through extensive experiments on simulated and real-world datasets. In particular, we demonstrate that the effectiveness of our proposed hierarchical RL-based method lies in its ability to capture such hierarchically-structured intent. As a result, the proposed HRL model achieves superior performance on several public datasets, compared with state-of-art baselines.

We present BYOL-Explore, a conceptually simple yet general approach for curiosity-driven exploration in visually-complex environments. BYOL-Explore learns a world representation, the world dynamics, and an exploration policy all-together by optimizing a single prediction loss in the latent space with no additional auxiliary objective. We show that BYOL-Explore is effective in DM-HARD-8, a challenging partially-observable continuous-action hard-exploration benchmark with visually-rich 3-D environments. On this benchmark, we solve the majority of the tasks purely through augmenting the extrinsic reward with BYOL-Explore s intrinsic reward, whereas prior work could only get off the ground with human demonstrations. As further evidence of the generality of BYOL-Explore, we show that it achieves superhuman performance on the ten hardest exploration games in Atari while having a much simpler design than other competitive agents.

Balancing exploration and exploitation remains a central challenge in reinforcement learning with verifiable rewards (RLVR) for large language models (LLMs). Current RLVR methods often overemphasize exploitation, leading to entropy collapse, diminished exploratory capacity, and ultimately limited performance gains. Although techniques that increase policy stochasticity can promote exploration, they frequently fail to escape dominant behavioral modes. This creates a self-reinforcing loop-repeatedly sampling and rewarding dominant modes-that further erodes exploration. We introduce Exploration-Enhanced Policy Optimization (EEPO), a framework that promotes exploration via two-stage rollouts with adaptive unlearning. In the first stage, the model generates half of the trajectories; it then undergoes a lightweight unlearning step to temporarily suppress these sampled responses, forcing the second stage to explore different regions of the output space. This sample-then-forget mechanism disrupts the self-reinforcing loop and promotes wider exploration during rollouts. Across five reasoning benchmarks, EEPO outperforms GRPO, achieving average relative gains of 24.3% on Qwen2.5-3B, 33.0% on Llama3.2-3B-Instruct, and 10.4% on Qwen3-8B-Base.

The standard post-training recipe for large reasoning models, supervised fine-tuning followed by reinforcement learning (SFT-then-RL), may limit the benefits of the RL stage: while SFT imitates expert demonstrations, it often causes overconfidence and reduces generation diversity, leaving RL with a narrowed solution space to explore. Adding entropy regularization during SFT is not a cure-all; it tends to flatten token distributions toward uniformity, increasing entropy without improving meaningful exploration capability. In this paper, we propose CurioSFT, an entropy-preserving SFT method designed to enhance exploration capabilities through intrinsic curiosity. It consists of (a) Self-Exploratory Distillation, which distills the model toward a self-generated, temperature-scaled teacher to encourage exploration within its capability; and (b) Entropy-Guided Temperature Selection, which adaptively adjusts distillation strength to mitigate knowledge forgetting by amplifying exploration at reasoning tokens while stabilizing factual tokens. Extensive experiments on mathematical reasoning tasks demonstrate that, in SFT stage, CurioSFT outperforms the vanilla SFT by 2.5 points on in-distribution tasks and 2.9 points on out-of-distribution tasks. We also verify that exploration capabilities preserved during SFT successfully translate into concrete gains in RL stage, yielding an average improvement of 5.0 points.

The human intrinsic desire to pursue knowledge, also known as curiosity, is considered essential in the process of skill acquisition. With the aid of artificial curiosity, we could equip current techniques for control, such as Reinforcement Learning, with more natural exploration capabilities. A promising approach in this respect has consisted of using Bayesian surprise on model parameters, i.e. a metric for the difference between prior and posterior beliefs, to favour exploration. In this contribution, we propose to apply Bayesian surprise in a latent space representing the agent's current understanding of the dynamics of the system, drastically reducing the computational costs. We extensively evaluate our method by measuring the agent's performance in terms of environment exploration, for continuous tasks, and looking at the game scores achieved, for video games. Our model is computationally cheap and compares positively with current state-of-the-art methods on several problems. We also investigate the effects caused by stochasticity in the environment, which is often a failure case for curiosity-driven agents. In this regime, the results suggest that our approach is resilient to stochastic transitions.

Reinforcement learning with verifiable rewards (RLVR) has proven effective in enhancing the reasoning of large language models (LLMs). Monte Carlo Tree Search (MCTS)-based extensions improve upon vanilla RLVR (e.g., GRPO) by providing tree-based reasoning rollouts that enable fine-grained and segment-level credit assignment. However, existing methods still suffer from limited exploration diversity and inefficient reasoning. To address the above challenges, we propose reinforced efficient reasoning via semantically diverse explorations, i.e., ROSE, for LLMs. To encourage more diverse reasoning exploration, our method incorporates a semantic-entropy-based branching strategy and an varepsilon-exploration mechanism. The former operates on already sampled reasoning rollouts to capture semantic uncertainty and select branching points with high semantic divergence to generate new successive reasoning paths, whereas the latter stochastically initiates reasoning rollouts from the root, preventing the search process from becoming overly local. To improve efficiency, we design a length-aware segment-level advantage estimator that rewards concise and correct reasoning while penalizing unnecessarily long reasoning chains. Extensive experiments on various mathematical reasoning benchmarks with Qwen and Llama models validate the effectiveness and efficiency of ROSE. Codes are available at https://github.com/ZiqiZhao1/ROSE-rl.

In the absence of extensive human-annotated data for complex reasoning tasks, self-improvement -- where models are trained on their own outputs -- has emerged as a primary method for enhancing performance. However, the critical factors underlying the mechanism of these iterative self-improving methods remain poorly understood, such as under what conditions self-improvement is effective, and what are the bottlenecks in the current iterations. In this work, we identify and propose methods to monitor two pivotal factors in this iterative process: (1) the model's ability to generate sufficiently diverse responses (exploration); and (2) the effectiveness of external rewards in distinguishing high-quality candidates from lower-quality ones (exploitation). Using mathematical reasoning as a case study, we begin with a quantitative analysis to track the dynamics of exploration and exploitation, discovering that a model's exploratory capabilities rapidly deteriorate over iterations, and the effectiveness of exploiting external rewards diminishes as well. Motivated by these findings, we introduce B-STaR, a Self-Taught Reasoning framework that autonomously adjusts configurations across iterations to Balance exploration and exploitation, thereby optimizing the self-improving effectiveness based on the current policy model and available rewards. Our experiments on mathematical reasoning, coding, and commonsense reasoning demonstrate that B-STaR not only enhances the model's exploratory capabilities throughout training but also achieves a more effective balance between exploration and exploitation, leading to superior performance.

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for enhancing reasoning and agentic behavior in large language models. However, rollout-intensive policy optimization is often limited by insufficient reward contrast, arising when overly simple or complex prompts generate low-variance feedback and when outcome-only rewards assign the same terminal assessment to every decision in a multi-turn rollout. Past efforts have focused on allocating available rollout resources to promising prompts, yet they only leverage sample informativeness at the prompt level and neglect variation in prefix-level informativeness across turns within the same rollout. This work targets multi-turn agentic RL by modeling each ReAct-style thought-action-observation turn as a semantically distinct node, allowing budget allocation to extend from prompt roots to turn-level prefixes with further continuations, which naturally forms tree-structured rollouts. We introduce Tree Rollout Allocation for Contrastive Exploration (TRACE), a unified rollout allocation framework that enhances reward contrast within a fixed sampling budget. Technically, TRACE allocates rollout budget to both prompt roots and intermediate prefixes that are most likely to yield mixed terminal rewards. A shared generalizable predictor estimates conditional success probability at these anchors from prefix histories to guide this allocation. The resulting adaptive tree structure enriches outcome-only feedback and amplifies the policy-update signal. Empirically, TRACE achieves competitive performance and efficiency gains on typical agentic benchmarks, e.g., improving Qwen3-14B Multi-Hop QA average accuracy by 2.8 points over competitive baselines at equal sampling cost.

Go-Explore is a powerful family of algorithms designed to solve hard-exploration problems, built on the principle of archiving discovered states, and iteratively returning to and exploring from the most promising states. This approach has led to superhuman performance across a wide variety of challenging problems including Atari games and robotic control, but requires manually designing heuristics to guide exploration, which is time-consuming and infeasible in general. To resolve this, we propose Intelligent Go-Explore (IGE) which greatly extends the scope of the original Go-Explore by replacing these heuristics with the intelligence and internalized human notions of interestingness captured by giant foundation models (FMs). This provides IGE with a human-like ability to instinctively identify how interesting or promising any new state is (e.g. discovering new objects, locations, or behaviors), even in complex environments where heuristics are hard to define. Moreover, IGE offers the exciting and previously impossible opportunity to recognize and capitalize on serendipitous discoveries that cannot be predicted ahead of time. We evaluate IGE on a range of language-based tasks that require search and exploration. In Game of 24, a multistep mathematical reasoning problem, IGE reaches 100% success rate 70.8% faster than the best classic graph search baseline. Next, in BabyAI-Text, a challenging partially observable gridworld, IGE exceeds the previous SOTA with orders of magnitude fewer online samples. Finally, in TextWorld, we show the unique ability of IGE to succeed in settings requiring long-horizon exploration where prior SOTA FM agents like Reflexion completely fail. Overall, IGE combines the tremendous strengths of FMs and the powerful Go-Explore algorithm, opening up a new frontier of research into creating more generally capable agents with impressive exploration capabilities.

Previous methods evaluate reward models by testing them on a fixed pairwise ranking test set, but they typically do not provide performance information on each preference dimension. In this work, we address the evaluation challenge of reward models by probing preference representations. To confirm the effectiveness of this evaluation method, we construct a Multi-dimensional Reward Model Benchmark (MRMBench), a collection of six probing tasks for different preference dimensions. We design it to favor and encourage reward models that better capture preferences across different dimensions. Furthermore, we introduce an analysis method, inference-time probing, which identifies the dimensions used during the reward prediction and enhances its interpretability. Through extensive experiments, we find that MRMBench strongly correlates with the alignment performance of large language models (LLMs), making it a reliable reference for developing advanced reward models. Our analysis of MRMBench evaluation results reveals that reward models often struggle to capture preferences across multiple dimensions, highlighting the potential of multi-objective optimization in reward modeling. Additionally, our findings show that the proposed inference-time probing method offers a reliable metric for assessing the confidence of reward predictions, which ultimately improves the alignment of LLMs.

Reinforcement Learning (RL) with rubric-based rewards has recently shown remarkable progress in enhancing general reasoning capabilities of Large Language Models (LLMs), yet still suffers from ineffective exploration confined to curent policy distribution. In fact, RL optimization can be viewed as steering the policy toward an ideal distribution that maximizes the rewards, while effective exploration should align efforts with desired target. Leveraging this insight, we propose HeRL, a Hindsight experience guided Reinforcement Learning framework to bootstrap effective exploration by explicitly telling LLMs the desired behaviors specified in rewards. Concretely, HeRL treats failed trajectories along with their unmet rubrics as hindsight experience, which serves as in-context guidance for the policy to explore desired responses beyond its current distribution. Additionally, we introduce a bonus reward to incentivize responses with greater potential for improvement under such guidance. HeRL facilitates effective learning from desired high quality samples without repeated trial-and-error from scratch, yielding a more accurate estimation of the expected gradient theoretically. Extensive experiments across various benchmarks demonstrate that HeRL achieves superior performance gains over baselines, and can further benefit from experience guided self-improvement at test time. Our code is available at https://github.com/sikelifei/HeRL.

Reward-based optimization algorithms require both exploration, to find rewards, and exploitation, to maximize performance. The need for efficient exploration is even more significant in sparse reward settings, in which performance feedback is given sparingly, thus rendering it unsuitable for guiding the search process. In this work, we introduce the SparsE Reward Exploration via Novelty and Emitters (SERENE) algorithm, capable of efficiently exploring a search space, as well as optimizing rewards found in potentially disparate areas. Contrary to existing emitters-based approaches, SERENE separates the search space exploration and reward exploitation into two alternating processes. The first process performs exploration through Novelty Search, a divergent search algorithm. The second one exploits discovered reward areas through emitters, i.e. local instances of population-based optimization algorithms. A meta-scheduler allocates a global computational budget by alternating between the two processes, ensuring the discovery and efficient exploitation of disjoint reward areas. SERENE returns both a collection of diverse solutions covering the search space and a collection of high-performing solutions for each distinct reward area. We evaluate SERENE on various sparse reward environments and show it compares favorably to existing baselines.

Large language models have demonstrated impressive reasoning capabilities, yet they often suffer from inefficiencies due to unnecessarily verbose or redundant outputs. While many works have explored reinforcement learning (RL) to enhance reasoning abilities, most primarily focus on improving accuracy, with limited attention to reasoning efficiency. Some existing approaches introduce direct length-based rewards to encourage brevity, but this often leads to noticeable drops in accuracy. In this paper, we propose Bingo, an RL framework that advances length-based reward design to boost efficient reasoning. Bingo incorporates two key mechanisms: a significance-aware length reward, which gradually guides the model to reduce only insignificant tokens, and a dynamic length reward, which initially encourages elaborate reasoning for hard questions but decays over time to improve overall efficiency. Experiments across multiple reasoning benchmarks show that Bingo improves both accuracy and efficiency. It outperforms the vanilla reward and several other length-based reward baselines in RL, achieving a favorable trade-off between accuracy and efficiency. These results underscore the potential of training LLMs explicitly for efficient reasoning.

We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. In this work, we study the maximum entropy exploration problem of two different types. The first type is visitation entropy maximization previously considered by Hazan et al.(2019) in the discounted setting. For this type of exploration, we propose a game-theoretic algorithm that has mathcal{O}(H^3S^2A/varepsilon^2) sample complexity thus improving the varepsilon-dependence upon existing results, where S is a number of states, A is a number of actions, H is an episode length, and varepsilon is a desired accuracy. The second type of entropy we study is the trajectory entropy. This objective function is closely related to the entropy-regularized MDPs, and we propose a simple algorithm that has a sample complexity of order mathcal{O}(poly(S,A,H)/varepsilon). Interestingly, it is the first theoretical result in RL literature that establishes the potential statistical advantage of regularized MDPs for exploration. Finally, we apply developed regularization techniques to reduce sample complexity of visitation entropy maximization to mathcal{O}(H^2SA/varepsilon^2), yielding a statistical separation between maximum entropy exploration and reward-free exploration.

Despite the great interest in the bandit problem, designing efficient algorithms for complex models remains challenging, as there is typically no analytical way to quantify uncertainty. In this paper, we propose Multiplier Bootstrap-based Exploration (MBE), a novel exploration strategy that is applicable to any reward model amenable to weighted loss minimization. We prove both instance-dependent and instance-independent rate-optimal regret bounds for MBE in sub-Gaussian multi-armed bandits. With extensive simulation and real data experiments, we show the generality and adaptivity of MBE.

A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, potentially improving credit assignment over outcome reward models (ORMs) that only provide feedback at the final step. However, collecting dense, per-step human labels is not scalable, and training PRMs from automatically-labeled data has thus far led to limited gains. To improve a base policy by running search against a PRM or using it as dense rewards for reinforcement learning (RL), we ask: "How should we design process rewards?". Our key insight is that, to be effective, the process reward for a step should measure progress: a change in the likelihood of producing a correct response in the future, before and after taking the step, corresponding to the notion of step-level advantages in RL. Crucially, this progress should be measured under a prover policy distinct from the base policy. We theoretically characterize the set of good provers and our results show that optimizing process rewards from such provers improves exploration during test-time search and online RL. In fact, our characterization shows that weak prover policies can substantially improve a stronger base policy, which we also observe empirically. We validate our claims by training process advantage verifiers (PAVs) to predict progress under such provers, and show that compared to ORMs, test-time search against PAVs is >8% more accurate, and 1.5-5times more compute-efficient. Online RL with dense rewards from PAVs enables one of the first results with 5-6times gain in sample efficiency, and >6% gain in accuracy, over ORMs.

In deep reinforcement learning (RL) research, there has been a concerted effort to design more efficient and productive exploration methods while solving sparse-reward problems. These exploration methods often share common principles (e.g., improving diversity) and implementation details (e.g., intrinsic reward). Prior work found that non-stationary Markov decision processes (MDPs) require exploration to efficiently adapt to changes in the environment with online transfer learning. However, the relationship between specific exploration characteristics and effective transfer learning in deep RL has not been characterized. In this work, we seek to understand the relationships between salient exploration characteristics and improved performance and efficiency in transfer learning. We test eleven popular exploration algorithms on a variety of transfer types -- or ``novelties'' -- to identify the characteristics that positively affect online transfer learning. Our analysis shows that some characteristics correlate with improved performance and efficiency across a wide range of transfer tasks, while others only improve transfer performance with respect to specific environment changes. From our analysis, make recommendations about which exploration algorithm characteristics are best suited to specific transfer situations.

While Large Language Models (LLMs) hold promise to become autonomous agents, they often explore suboptimally in sequential decision-making. Recent work has sought to enhance this capability via supervised fine-tuning (SFT) or reinforcement learning (RL), improving regret on the classic multi-armed bandit task. However, it remains unclear how these learning methods shape exploration strategies and how well they generalize. We investigate both paradigms by training LLMs with SFT on expert trajectories and RL with a range of tailored reward signals including a strategic, regret-shaped reward to reduce variance, and an algorithmic reward that enables oracle imitation. The resulting agents outperform pre-trained models and achieve performance comparable to Upper Confidence Bound (UCB) and Thompson Sampling, with robust generalization to 6x longer horizons and across bandit families. Behavioral analysis reveals that gains often stem from more sophisticated but greedier exploitation: RL/SFT agents are more prone to early catastrophic failure than pre-trained models, prematurely abandoning exploration. Furthermore, agents trained to imitate UCB learn to outperform their teacher by adopting more exploitative variants. Our findings clarify when each training paradigm is preferable and advocate tailored reward design and evaluation beyond average regret to promote robust exploratory behavior.

Balancing exploration and exploitation is a central goal in reinforcement learning (RL). Despite recent advances in enhancing language model (LM) reasoning, most methods lean toward exploitation, and increasingly encounter performance plateaus. In this work, we revisit entropy -- a signal of exploration in RL -- and examine its relationship to exploratory reasoning in LMs. Through empirical analysis, we uncover strong positive correlations between high-entropy regions and three types of exploratory reasoning actions: (1) pivotal tokens that determine or connect logical steps, (2) reflective actions such as self-verification and correction, and (3) rare behaviors under-explored by the base LMs. Motivated by this, we introduce a minimal modification to standard RL with only one line of code: augmenting the advantage function with an entropy-based term. Unlike traditional maximum-entropy methods which encourage exploration by promoting uncertainty, we encourage exploration by promoting longer and deeper reasoning chains. Notably, our method achieves significant gains on the Pass@K metric -- an upper-bound estimator of LM reasoning capabilities -- even when evaluated with extremely large K values, pushing the boundaries of LM reasoning.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs). Unlike traditional RL approaches, RLVR leverages rule-based feedback to guide LLMs in generating and refining complex reasoning chains -- a process critically dependent on effective exploration strategies. While prior work has demonstrated RLVR's empirical success, the fundamental mechanisms governing LLMs' exploration behaviors remain underexplored. This technical report presents a systematic investigation of exploration capacities in RLVR, covering four main aspects: (1) exploration space shaping, where we develop quantitative metrics to characterize LLMs' capability boundaries; (2) entropy-performance exchange, analyzed across training stages, individual instances, and token-level patterns; and (3) RL performance optimization, examining methods to effectively translate exploration gains into measurable improvements. By unifying previously identified insights with new empirical evidence, this work aims to provide a foundational framework for advancing RLVR systems.

Recommender systems must balance personalization, diversity, and robustness to cold-start scenarios to remain effective in dynamic content environments. This paper introduces an adaptive, exploration-based recommendation framework that adjusts to evolving user preferences and content distributions to promote diversity and novelty without compromising relevance. The system represents items using sentence-transformer embeddings and organizes them into semantically coherent clusters through an online algorithm with adaptive thresholding. A user-controlled exploration mechanism enhances diversity by selectively sampling from under-explored clusters. Experiments on the MovieLens dataset show that enabling exploration reduces intra-list similarity from 0.34 to 0.26 and increases unexpectedness to 0.73, outperforming collaborative filtering and popularity-based baselines. A/B testing with 300 simulated users reveals a strong link between interaction history and preference for diversity, with 72.7% of long-term users favoring exploratory recommendations. Computational analysis confirms that clustering and recommendation processes scale linearly with the number of clusters. These results demonstrate that adaptive exploration effectively mitigates over-specialization while preserving personalization and efficiency.

Fine-tuning large language models (LLMs) on reasoning benchmarks via reinforcement learning requires a specific reward function, often binary, for each benchmark. This comes with two potential limitations: the need to design the reward, and the potentially sparse nature of binary rewards. Here, we systematically investigate rewards derived from the probability or log-probability of emitting the reference answer (or any other prompt continuation present in the data), which have the advantage of not relying on specific verifiers and being available at scale. Several recent works have advocated for the use of similar rewards (e.g., VeriFree, JEPO, RLPR, NOVER). We systematically compare variants of likelihood-based rewards with standard baselines, testing performance both on standard mathematical reasoning benchmarks, and on long-form answers where no external verifier is available. We find that using the log-probability of the reference answer as the reward for chain-of-thought (CoT) learning is the only option that performs well in all setups. This reward is also consistent with the next-token log-likelihood loss used during pretraining. In verifiable settings, log-probability rewards bring comparable or better success rates than reinforcing with standard binary rewards, and yield much better perplexity. In non-verifiable settings, they perform on par with SFT. On the other hand, methods based on probability, such as VeriFree, flatline on non-verifiable settings due to vanishing probabilities of getting the correct answer. Overall, this establishes log-probability rewards as a viable method for CoT fine-tuning, bridging the short, verifiable and long, non-verifiable answer settings.

This paper examines the exploration-exploitation trade-off in reinforcement learning with verifiable rewards (RLVR), a framework for improving the reasoning of Large Language Models (LLMs). Recent studies suggest that RLVR can elicit strong mathematical reasoning in LLMs through two seemingly paradoxical mechanisms: spurious rewards, which suppress exploitation by rewarding outcomes unrelated to the ground truth, and entropy minimization, which suppresses exploration by pushing the model toward more confident and deterministic outputs, highlighting a puzzling dynamic: both discouraging exploitation and discouraging exploration improve reasoning performance, yet the underlying principles that reconcile these effects remain poorly understood. We focus on two fundamental questions: (i) how policy entropy relates to performance, and (ii) whether spurious rewards yield gains, potentially through the interplay of clipping bias and model contamination. Our results show that clipping bias under spurious rewards reduces policy entropy, leading to more confident and deterministic outputs, while entropy minimization alone is insufficient for improvement. We further propose a reward-misalignment model explaining why spurious rewards can enhance performance beyond contaminated settings. Our findings clarify the mechanisms behind spurious-reward benefits and provide principles for more effective RLVR training.

Reinforcement learning with verifiable rewards (RLVR) improves reasoning in large language models (LLMs) but struggles with exploration, an issue that still persists for multimodal LLMs (MLLMs). Current methods treat the visual input as a fixed, deterministic condition, overlooking a critical source of ambiguity and struggling to build policies robust to plausible visual variations. We introduce VOGUE (Visual Uncertainty Guided Exploration), a novel method that shifts exploration from the output (text) to the input (visual) space. By treating the image as a stochastic context, VOGUE quantifies the policy's sensitivity to visual perturbations using the symmetric KL divergence between a "raw" and "noisy" branch, creating a direct signal for uncertainty-aware exploration. This signal shapes the learning objective via an uncertainty-proportional bonus, which, combined with a token-entropy bonus and an annealed sampling schedule, effectively balances exploration and exploitation. Implemented within GRPO on two model scales (Qwen2.5-VL-3B/7B), VOGUE boosts pass@1 accuracy by an average of 2.6% on three visual math benchmarks and 3.7% on three general-domain reasoning benchmarks, while simultaneously increasing pass@4 performance and mitigating the exploration decay commonly observed in RL fine-tuning. Our work shows that grounding exploration in the inherent uncertainty of visual inputs is an effective strategy for improving multimodal reasoning.

Repeated Sampling (RS) is a simple inference-time algorithm that has been shown to improve model performance on complex tasks. Although it is an effective way of scaling inference time, it often struggles to generate diverse solution candidates, frequently relying on the same underlying approach to solve the problem and thus producing redundant samples. To address this limitation, we propose a new inference algorithm, GuidedSampling, which decouples the exploration and generation phases during inference, increasing diversity of generated candidate solutions. The exploration phase identifies multiple concepts that can be utilized to solve the problem, while the generation phase applies a specific concept to provide final solution candidates. We first define the theoretical bounds of GuidedSampling and then empirically demonstrate that it improves the performance of base model at pass@50 by on an average ~21.6% across various benchmarks compared to RS. Furthermore, models trained on trajectories of GuidedSampling exhibit substantial performance improvements at pass@5 by on an average ~9.7%, compared to models trained on traditional RS. Additionally, models trained with GuidedSampling increases the average number of concepts per instance (1.67 -> 3.03), yielding a diverse set of candidates than traditional RS.

Despite progress in video understanding, current MLLMs struggle with counting tasks. Existing benchmarks are limited by short videos, close-set queries, lack of clue annotations, and weak multimodal coverage. In this paper, we introduce CG-AV-Counting, a manually-annotated clue-grounded counting benchmark with 1,027 multimodal questions and 5,845 annotated clues over 497 long videos. It supports both black-box and white-box evaluation, serving as a comprehensive testbed for both end-to-end and reasoning-based counting. To explore ways to improve model's counting capability, we propose AV-Reasoner, a model trained with GRPO and curriculum learning to generalize counting ability from related tasks. AV-Reasoner achieves state-of-the-art results across multiple benchmarks, demonstrating the effectiveness of reinforcement learning. However, experiments show that on out-of-domain benchmarks, reasoning in the language space fails to bring performance gains. The code and benchmark have been realeased on https://av-reasoner.github.io.

Reinforcement learning has empowered large language models to act as intelligent agents, yet training them for long-horizon tasks remains challenging due to the scarcity of high-quality trajectories, especially under limited resources. Existing methods typically scale up rollout sizes and indiscriminately allocate computational resources among intermediate steps. Such attempts inherently waste substantial computation budget on trivial steps while failing to guarantee sample quality. To address this, we propose Spark (Strategic Policy-Aware exploRation via Key-state dynamic branching), a novel framework that selectively branches at critical decision states for resource-efficient exploration. Our key insight is to activate adaptive branching exploration at critical decision points to probe promising trajectories, thereby achieving precise resource allocation that prioritizes sampling quality over blind coverage. This design leverages the agent's intrinsic decision-making signals to reduce dependence on human priors, enabling the agent to autonomously expand exploration and achieve stronger generalization. Experiments across diverse tasks (e.g., embodied planning), demonstrate that Spark achieves superior success rates with significantly fewer training samples, exhibiting robust generalization even in unseen scenarios.

The ongoing debate on whether reinforcement learning with verifiable rewards (RLVR) expands or shrinks the reasoning capabilities of large language models (LLMs) remains unresolved. Some studies contend that RLVR mainly improves sampling efficiency but at the expense of diversity and exploratory capacity, resulting in capability boundary shrinkage. In contrast, others demonstrate that prolonged training can lead to the emergence of novel reasoning strategies, suggesting capability boundary expansion. To reconcile these contradictory findings, we theoretically and empirically show that both perspectives are partially valid-each aligning with a separate phase in an inherent two-stage probability mass dynamic: (1) Exploitation stage: initially, the model primarily samples explored high-reward and low-reward tokens, while rarely selecting the potentially optimal token. Positive advantage estimates increase the probability of high-reward tokens and decrease those of low-reward tokens, yet the optimal token's probability remains largely unchanged during this stage. (2) Exploration stage: as training advances, the growth rate of previously acquired high-reward tokens slows as their probabilities approach saturation. When a potentially optimal token-now receiving positive advantage estimates-is occasionally sampled, its probability increases, while those of the originally high-reward tokens decrease. This dynamic suggests that over-exploitation during the exploitation stage may lead to capability boundary shrinkage, whereas prolonged training into the exploration stage can promote an expansion of the reasoning capability boundary. Building upon our insights, we revisit the potential of only using relative negative gradients for prolonging training, providing a theoretical and empirical foundation for the development of more advanced reasoning capabilities.

Research Agents enable models to gather information from the web using tools to answer user queries, requiring them to dynamically interleave internal reasoning with tool use. While such capabilities can in principle be learned via reinforcement learning with verifiable rewards (RLVR), we observe that agents often exhibit poor exploration behaviors, including premature termination and biased tool usage. As a result, RLVR alone yields limited improvements. We propose SynPlanResearch-R1, a framework that synthesizes tool-use trajectories that encourage deeper exploration to shape exploration during cold-start supervised fine-tuning, providing a strong initialization for subsequent RL. Across seven multi-hop and open-web benchmarks, \framework improves performance by up to 6.0% on Qwen3-8B and 5.8% on Qwen3-4B backbones respectively compared to SOTA baselines. Further analyses of tool-use patterns and training dynamics compared to baselines shed light on the factors underlying these gains. Our code is publicly available at https://github.com/HansiZeng/syn-plan-research.

Recent advancements in agentic test-time scaling allow models to gather environmental feedback before committing to final actions. A key limitation of existing methods is that they typically employ undifferentiated exploration strategies, lacking the ability to adaptively distinguish when exploration is truly required. In this paper, we propose an exploration-aware reinforcement learning framework that enables LLM agents to adaptively explore only when uncertainty is high. Our method introduces a fine-grained reward function via variational inference that explicitly evaluates exploratory actions by estimating their potential to improve future decision-making, together with an exploration-aware grouping mechanism that separates exploratory actions from task-completion actions during optimization. By targeting informational gaps, this design allows agents to explore selectively and transition to execution as soon as the task context is clear. Empirically, we demonstrate that our approach achieves consistent improvements across a range of challenging text-based and GUI-based agent benchmarks. Code is available at https://github.com/HansenHua/EAPO-ICML26 and models are available at https://huggingface.co/hansenhua/EAPO-ICML26.

In this paper, we introduce Latent Go-Explore (LGE), a simple and general approach based on the Go-Explore paradigm for exploration in reinforcement learning (RL). Go-Explore was initially introduced with a strong domain knowledge constraint for partitioning the state space into cells. However, in most real-world scenarios, drawing domain knowledge from raw observations is complex and tedious. If the cell partitioning is not informative enough, Go-Explore can completely fail to explore the environment. We argue that the Go-Explore approach can be generalized to any environment without domain knowledge and without cells by exploiting a learned latent representation. Thus, we show that LGE can be flexibly combined with any strategy for learning a latent representation. Our results indicate that LGE, although simpler than Go-Explore, is more robust and outperforms state-of-the-art algorithms in terms of pure exploration on multiple hard-exploration environments including Montezuma's Revenge. The LGE implementation is available as open-source at https://github.com/qgallouedec/lge.

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a powerful paradigm for enhancing the complex reasoning capabilities of Large Reasoning Models. However, standard outcome-based supervision suffers from a critical limitation that penalizes trajectories that are largely correct but fail due to several missteps as heavily as completely erroneous ones. This coarse feedback signal causes the model to discard valuable largely correct rollouts, leading to a degradation in rollout diversity that prematurely narrows the exploration space. Process Reward Models have demonstrated efficacy in providing reliable step-wise verification for test-time scaling, naively integrating these signals into RLVR as dense rewards proves ineffective.Prior methods attempt to introduce off-policy guided whole-trajectory replacement that often outside the policy model's distribution, but still fail to utilize the largely correct rollouts generated by the model itself and thus do not effectively mitigate the narrowing of the exploration space. To address these issues, we propose SCOPE (Step-wise Correction for On-Policy Exploration), a novel framework that utilizes Process Reward Models to pinpoint the first erroneous step in suboptimal rollouts and applies fine-grained, step-wise off-policy rectification. By applying precise refinement on partially correct rollout, our method effectively salvages partially correct trajectories and increases diversity score by 13.5%, thereby sustaining a broad exploration space. Extensive experiments demonstrate that our approach establishes new state-of-the-art results, achieving an average accuracy of 46.6% on math reasoning and exhibiting robust generalization with 53.4% accuracy on out-of-distribution reasoning tasks.

One of the challenges in online reinforcement learning (RL) is that the agent needs to trade off the exploration of the environment and the exploitation of the samples to optimize its behavior. Whether we optimize for regret, sample complexity, state-space coverage or model estimation, we need to strike a different exploration-exploitation trade-off. In this paper, we propose to tackle the exploration-exploitation problem following a decoupled approach composed of: 1) An "objective-specific" algorithm that (adaptively) prescribes how many samples to collect at which states, as if it has access to a generative model (i.e., a simulator of the environment); 2) An "objective-agnostic" sample collection exploration strategy responsible for generating the prescribed samples as fast as possible. Building on recent methods for exploration in the stochastic shortest path problem, we first provide an algorithm that, given as input the number of samples b(s,a) needed in each state-action pair, requires O(B D + D^{3/2} S^2 A) time steps to collect the B=sum_{s,a} b(s,a) desired samples, in any unknown communicating MDP with S states, A actions and diameter D. Then we show how this general-purpose exploration algorithm can be paired with "objective-specific" strategies that prescribe the sample requirements to tackle a variety of settings -- e.g., model estimation, sparse reward discovery, goal-free cost-free exploration in communicating MDPs -- for which we obtain improved or novel sample complexity guarantees.

In this work, we study the simple yet universally applicable case of reward shaping in value-based Deep Reinforcement Learning (DRL). We show that reward shifting in the form of the linear transformation is equivalent to changing the initialization of the Q-function in function approximation. Based on such an equivalence, we bring the key insight that a positive reward shifting leads to conservative exploitation, while a negative reward shifting leads to curiosity-driven exploration. Accordingly, conservative exploitation improves offline RL value estimation, and optimistic value estimation improves exploration for online RL. We validate our insight on a range of RL tasks and show its improvement over baselines: (1) In offline RL, the conservative exploitation leads to improved performance based on off-the-shelf algorithms; (2) In online continuous control, multiple value functions with different shifting constants can be used to tackle the exploration-exploitation dilemma for better sample efficiency; (3) In discrete control tasks, a negative reward shifting yields an improvement over the curiosity-based exploration method.

In recommender system or crowdsourcing applications of online learning, a human's preferences or abilities are often a function of the algorithm's recent actions. Motivated by this, a significant line of work has formalized settings where an action's loss is a function of the number of times that action was recently played in the prior m timesteps, where m corresponds to a bound on human memory capacity. To more faithfully capture decay of human memory with time, we introduce the Weighted Tallying Bandit (WTB), which generalizes this setting by requiring that an action's loss is a function of a weighted summation of the number of times that arm was played in the last m timesteps. This WTB setting is intractable without further assumption. So we study it under Repeated Exposure Optimality (REO), a condition motivated by the literature on human physiology, which requires the existence of an action that when repetitively played will eventually yield smaller loss than any other sequence of actions. We study the minimization of the complete policy regret (CPR), which is the strongest notion of regret, in WTB under REO. Since m is typically unknown, we assume we only have access to an upper bound M on m. We show that for problems with K actions and horizon T, a simple modification of the successive elimination algorithm has O left( KT + (m+M)K right) CPR. Interestingly, upto an additive (in lieu of mutliplicative) factor in (m+M)K, this recovers the classical guarantee for the simpler stochastic multi-armed bandit with traditional regret. We additionally show that in our setting, any algorithm will suffer additive CPR of Omega left( mK + M right), demonstrating our result is nearly optimal. Our algorithm is computationally efficient, and we experimentally demonstrate its practicality and superiority over natural baselines.

Performing Reinforcement Learning in sparse rewards settings, with very little prior knowledge, is a challenging problem since there is no signal to properly guide the learning process. In such situations, a good search strategy is fundamental. At the same time, not having to adapt the algorithm to every single problem is very desirable. Here we introduce TAXONS, a Task Agnostic eXploration of Outcome spaces through Novelty and Surprise algorithm. Based on a population-based divergent-search approach, it learns a set of diverse policies directly from high-dimensional observations, without any task-specific information. TAXONS builds a repertoire of policies while training an autoencoder on the high-dimensional observation of the final state of the system to build a low-dimensional outcome space. The learned outcome space, combined with the reconstruction error, is used to drive the search for new policies. Results show that TAXONS can find a diverse set of controllers, covering a good part of the ground-truth outcome space, while having no information about such space.

Reinforcement Learning with Verifiable Rewards (RLVR) has catalyzed significant advances in the reasoning capabilities of Large Language Models (LLMs). However, effectively managing the exploration and exploitation trade-off remains a critical challenge. In this paper, we fully analyze the exploration and exploitation dilemma of extremely hard and easy samples during the training and propose a new fine-grained trade-off mechanism. Concretely, we introduce a perplexity space disentangling strategy that divides the sample space into distinct exploration (high perplexity) and exploitation (low perplexity) subspaces, thereby mining fine-grained samples requiring exploration-exploitation trade-off. Subsequently, we propose a bidirectional reward allocation mechanism with a minimum impact on verification rewards to implement perplexity-guided exploration and exploitation, enabling more stable policy optimization. Finally, we have evaluated our method on two mainstream tasks: mathematical reasoning and function calling, and experimental results demonstrate the superiority of the proposed method, confirming its effectiveness in enhancing LLM performance by fine-grained exploration-exploitation trade-off.

Reinforcement learning (RL) algorithms aim to balance exploiting the current best strategy with exploring new options that could lead to higher rewards. Most common RL algorithms use undirected exploration, i.e., select random sequences of actions. Exploration can also be directed using intrinsic rewards, such as curiosity or model epistemic uncertainty. However, effectively balancing task and intrinsic rewards is challenging and often task-dependent. In this work, we introduce a framework, MaxInfoRL, for balancing intrinsic and extrinsic exploration. MaxInfoRL steers exploration towards informative transitions, by maximizing intrinsic rewards such as the information gain about the underlying task. When combined with Boltzmann exploration, this approach naturally trades off maximization of the value function with that of the entropy over states, rewards, and actions. We show that our approach achieves sublinear regret in the simplified setting of multi-armed bandits. We then apply this general formulation to a variety of off-policy model-free RL methods for continuous state-action spaces, yielding novel algorithms that achieve superior performance across hard exploration problems and complex scenarios such as visual control tasks.

Consider the problem of exploration in sparse-reward or reward-free environments, such as in Montezuma's Revenge. In the curiosity-driven paradigm, the agent is rewarded for how much each realized outcome differs from their predicted outcome. But using predictive error as intrinsic motivation is fragile in stochastic environments, as the agent may become trapped by high-entropy areas of the state-action space, such as a "noisy TV". In this work, we study a natural solution derived from structural causal models of the world: Our key idea is to learn representations of the future that capture precisely the unpredictable aspects of each outcome -- which we use as additional input for predictions, such that intrinsic rewards only reflect the predictable aspects of world dynamics. First, we propose incorporating such hindsight representations into models to disentangle "noise" from "novelty", yielding Curiosity in Hindsight: a simple and scalable generalization of curiosity that is robust to stochasticity. Second, we instantiate this framework for the recently introduced BYOL-Explore algorithm as our prime example, resulting in the noise-robust BYOL-Hindsight. Third, we illustrate its behavior under a variety of different stochasticities in a grid world, and find improvements over BYOL-Explore in hard-exploration Atari games with sticky actions. Notably, we show state-of-the-art results in exploring Montezuma's Revenge with sticky actions, while preserving performance in the non-sticky setting.

We systematically investigate all 25 public ARC-AGI-3 games and find that every one is reachable through non-intelligent strategies: 10 in a single blind step, 5 after one probing action, 1 via repeated ACTION1 presses, 1 via diverse exploration, and 8 via single repeated actions with sufficient budget (50-200 steps). A library-level null-coordinate vulnerability additionally bypasses 18 games in 1 step. This benchmark critique implies the public evaluation set cannot discriminate intelligent exploration from trivial heuristics - the private 55-game evaluation is the only genuine intelligence test. Against this backdrop, we present AERA (Adaptive Epistemic Reasoning Agent), a three-phase (EXPLORE / VERIFY / PLAN) agent achieving RHAE=0.2116 (4/25 solved) on these 25 games with Qwen2.5-0.5B, while random and no-explore baselines score 0.0000. We formalise AERA through a Speed--Depth trade-off framework: under a convexity assumption (proved for a class of environments in the Appendix), RHAE's quadratic form emerges as a second-order penalty for deviating from the Pareto frontier between action efficiency and information gain. Contributions: (i) a benchmark validity analysis showing that current interactive reasoning benchmarks fail to measure the exploration they claim to require, and (ii) the EXPLORE-before-PLAN framework and model-capability x exploration interaction. The linked code track entry achieves RHAE=0.30 on the full 55-game private evaluation. Code: CC0.

Small language models (SLMs) struggle with complex reasoning because exploration is expensive under tight compute budgets. We introduce Semantic Diversity-Exploration-Exploitation (SD-E^2), a reinforcement learning framework that makes exploration explicit by optimizing semantic diversity in generated reasoning trajectories. Using a frozen sentence-embedding model, SD-E^2 assigns a diversity reward that captures (i) the coverage of semantically distinct solution strategies and (ii) their average pairwise dissimilarity in embedding space, rather than surface-form novelty. This diversity reward is combined with outcome correctness and solution efficiency in a z-score-normalized multi-objective objective that stabilizes training. On GSM8K, SD-E^2 surpasses the base Qwen2.5-3B-Instruct and strong GRPO baselines (GRPO-CFL and GRPO-CFEE) by +27.4, +5.2, and +1.5 percentage points, respectively, while discovering on average 9.8 semantically distinct strategies per question. We further improve MedMCQA to 49.64% versus 38.37% for the base model and show gains on the harder AIME benchmark (1983-2025), reaching 13.28% versus 6.74% for the base. These results indicate that rewarding semantic novelty yields a more compute-efficient exploration-exploitation signal for training reasoning-capable SLMs. By introducing cognitive adaptation-adjusting the reasoning process structure rather than per-token computation-SD-E^2 offers a complementary path to efficiency gains in resource-constrained models.

Exploration is essential for reliable autonomy in multi-agent systems, yet it remains unclear whether large language model (LLM) agents can explore effectively when interacting with one another. We show that modern LLM agents fail to do so, often exhibiting myopic and polarized interaction patterns that lead to suboptimal coordination and increased regret. We formalize this challenge as the Multi-Agent Exploration problem, modeling it as a partially observable stochastic game (POSG) problem in which agents must probe peers to infer their capabilities and identify effective interaction strategies. To address this, we introduce Multi- Agent Contextual Exploration (MACE), a lightweight framework that explicitly promotes exploration through structured peer selection. Across both contextual and parametric diversity settings, MACE substantially improves exploration behavior and downstream task performance. We further show theoretically that the value of exploration increases with agent diversity. Overall, our results highlight a fundamental limitation of current LLM agents and underscore the importance of explicitly guided exploration for reliable multi-agent autonomy. Code will be released in https://github.com/deeplearning-wisc/mace

Recommender systems play a crucial role in internet economies by connecting users with relevant products. However, designing effective recommender systems faces the key challenges: the exploration-exploitation tradeoff in securing incentive to explore new products against user's self-interested preferences. While prior work addresses Bayesian Incentive Compatibility (BIC) in fixed-design linear bandits (Sellke & Slivkins, 2023), we tackle the challenge of stochastic user covariates sampled online. Unlike standard black-box reductions (Mansour et al., 2020), our two-stage framework exploits the linear reward structure to achieve sublinear regret while satisfying incentive constraints. To address it, we propose a two-stage algorithm that integrates incentivized exploration with any efficient plug-in offline learning algorithms. In the first stage, it explores products while maintaining incentive compatibility to gather optimal samples. The second stage employs inverse proportional gap sampling strategy (IPGS) integrated with any efficient learning methods to secure sublinear regret. Theoretically, we prove that algorithm RCB achieves O(KdT) regret and simultaneously satisfies incentive constraints, and discovers the tradeoff between incentive budget and regret, validating in experiments. We demonstrate RCB's strong incentive gain, sublinear regret, and robustness through a real application on personalized warfarin dosing and simulations.

Autonomous AI Research promises to accelerate the scientific progress of machine learning. To realise this goal, current Large Language Model (LLM)-based agents need to go beyond just writing code, to mastering the exploration of simultaneously performant, diverse and novel ideas. To this end, we introduce Heuresis, a framework that abstracts the research pipeline into a set of general and composable primitives, enabling open-ended scientific exploration in machine learning research. We implement six search strategies: a greedy baseline, two archive-based (MAP-Elites, Go-Explore), one evolutionary (Islands), and two divergent (Curiosity, Omni), and evaluate them across three axes (Quality, Diversity, and Novelty) on three domains (LLM Pretraining, On-Policy RL, and Model Unlearning), totalling 3,222 scored runs. We find that completely novel ideas are rare. No idea across our scored runs is rated as "Original", and only a few achieve only "Minor Similarity" to prior work. Moreover, novel ideas never approach the highest-performing known-recipe scores. Across all six strategies and three domains, only one such idea lands in the top-10 by quality. We also observed agents resorting to a variety of reward-hacking techniques during execution (40 confirmed fabrications across 1,628 scored runs), and detecting them was necessary to keep the search faithful to the task. Our results show that while current search and Quality-Diversity strategies enable us to steer where the generated ideas land on the quality, diversity, and novelty axes, they do not expand the quality-novelty frontier. Bridging this gap is the open challenge towards the ultimate goal of perpetual, autonomous scientific progress. Code is available at github.com/a-antoniades/Heuresis.

Reinforcement learning with verifiable rewards has significantly advanced the reasoning capabilities of large language models, yet how to explicitly steer training toward exploration or exploitation remains an open problem. We introduce Token Hidden Reward (THR), a token-level metric that quantifies each token's influence on the likelihood of correct responses under Group Relative Policy Optimization (GRPO). We find that training dynamics are dominated by a small subset of tokens with high absolute THR values. Most interestingly, tokens with positive THR strengthen confidence in correct outputs, thus favoring exploitation, while tokens with negative THR preserve probability mass for alternative outputs, enabling exploration. This insight suggests a natural intervention: a THR-guided reweighting algorithm that modulates GRPO's learning signals to explicitly bias training toward exploitation or exploration. We validate the efficacy of this algorithm on diverse math reasoning benchmarks. By amplifying tokens with positive THR value and weakening negative ones, our algorithm improves greedy-decoding accuracy, favoring exploitation. The reverse strategy yields consistent gains in Pass@K accuracy, favoring exploration. We further demonstrate that our algorithm integrates seamlessly with other RL objectives such as GSPO and generalizes across architectures including Llama. These findings establish THR as a principled and fine-grained mechanism for dynamically controlling exploration and exploitation in RL-tuned LLMs, providing new tools for targeted fine-tuning in reasoning-intensive applications.

Agentic reinforcement learning requires assigning credit to environment-facing actions such as searches, clicks, edits, navigation commands, and object interactions. Standard GRPO uses the final verifier outcome as a uniform advantage over all action tokens. This outcome signal is useful but structurally incomplete: it punishes useful exploration in failed rollouts and reinforces redundant or regressive actions in successful rollouts. We propose TRIAGE, a role-typed credit assignment framework that adds a semantic role axis to outcome credit. A structured judge classifies each segment as decisive progress, useful exploration, no-progress infrastructure, or regression, and a fixed role-conditioned rule maps these labels to bounded segment-level process rewards. This keeps verifier outcomes as the source of optimization direction while correcting the two main blind spots of outcome-only credit. We further show that role-conditioned credit is the optimal segment-level correction expressible from role labels alone -- a projection of the per-segment advantage residual onto the role variable -- so that the fixed role constants reduce advantage estimation error whenever the judge is reliable, and we connect this to lower-variance policy gradients. Across ALFWorld, Search-QA, and WebShop, TRIAGE improves success rates over GRPO for two policy models and outperforms both a scalar judge-derived process reward and an outcome-supervised shared-backbone value baseline. Ablations show that the gain comes from role typing rather than merely adding dense rewards: reliable detection of regression inside successful trajectories is the dominant contributor, while exploration credit provides a consistent secondary gain; on completed ALFWorld and WebShop rollouts, TRIAGE also reduces environment-facing turns by an additional 10.4% and 14.8% relative to GRPO.

We investigate the extent to which contemporary Large Language Models (LLMs) can engage in exploration, a core capability in reinforcement learning and decision making. We focus on native performance of existing LLMs, without training interventions. We deploy LLMs as agents in simple multi-armed bandit environments, specifying the environment description and interaction history entirely in-context, i.e., within the LLM prompt. We experiment with GPT-3.5, GPT-4, and Llama2, using a variety of prompt designs, and find that the models do not robustly engage in exploration without substantial interventions: i) Across all of our experiments, only one configuration resulted in satisfactory exploratory behavior: GPT-4 with chain-of-thought reasoning and an externally summarized interaction history, presented as sufficient statistics; ii) All other configurations did not result in robust exploratory behavior, including those with chain-of-thought reasoning but unsummarized history. Although these findings can be interpreted positively, they suggest that external summarization -- which may not be possible in more complex settings -- is important for obtaining desirable behavior from LLM agents. We conclude that non-trivial algorithmic interventions, such as fine-tuning or dataset curation, may be required to empower LLM-based decision making agents in complex settings.

The flexibility and accuracy of methods for automatically counting objects in images and videos are limited by the way the object can be specified. While existing methods allow users to describe the target object with text and visual examples, the visual examples must be manually annotated inside the image, and there is no way to specify what not to count. To address these gaps, we introduce novel capabilities that expand how the target object can be specified. Specifically, we extend the prompt to enable what not to count to be described with text and/or visual examples, introduce the concept of `pseudo-exemplars' that automate the annotation of visual examples at inference, and extend counting models to accept visual examples from both natural and synthetic external images. We also use our new counting model, CountGD++, as a vision expert agent for an LLM. Together, these contributions expand the prompt flexibility of multi-modal open-world counting and lead to significant improvements in accuracy, efficiency, and generalization across multiple datasets. Code is available at https://github.com/niki-amini-naieni/CountGDPlusPlus.

Reinforcement Learning from Verifiable Rewards (RLVR) improves the reasoning abilities of Large Language Models (LLMs) but it struggles with unstable exploration. We propose FR3E (First Return, Entropy-Eliciting Explore), a structured exploration framework that identifies high-uncertainty decision points in reasoning trajectories and performs targeted rollouts to construct semantically grounded intermediate feedback. Our method provides targeted guidance without relying on dense supervision. Empirical results on mathematical reasoning benchmarks(AIME24) show that FR3E promotes more stable training, produces longer and more coherent responses, and increases the proportion of fully correct trajectories. These results highlight the framework's effectiveness in improving LLM reasoning through more robust and structured exploration.

We present an approach called Q-probing to adapt a pre-trained language model to maximize a task-specific reward function. At a high level, Q-probing sits between heavier approaches such as finetuning and lighter approaches such as few shot prompting, but can also be combined with either. The idea is to learn a simple linear function on a model's embedding space that can be used to reweight candidate completions. We theoretically show that this sampling procedure is equivalent to a KL-constrained maximization of the Q-probe as the number of samples increases. To train the Q-probes we consider either reward modeling or a class of novel direct policy learning objectives based on importance weighted policy gradients. With this technique, we see gains in domains with ground-truth rewards (code generation) as well as implicit rewards defined by preference data, even outperforming finetuning in data-limited regimes. Moreover, a Q-probe can be trained on top of an API since it only assumes access to sampling and embeddings. Code: https://github.com/likenneth/q_probe .

We propose Strategy-aware Surprise (SuS), a novel intrinsic motivation framework that uses pre-post prediction mismatch as a novelty signal for exploration in reinforcement learning. Unlike traditional curiosity-driven methods that rely solely on state prediction error, SuS introduces two complementary components: Strategy Stability (SS) and Strategy Surprise (SuS). SS measures consistency in behavioral strategy across temporal steps, while SuS captures unexpected outcomes relative to the agent's current strategy representation. Our combined reward formulation leverages both signals through learned weighting coefficients. We evaluate SuS on mathematical reasoning tasks using large language models, demonstrating significant improvements in both accuracy and solution diversity. Ablation studies confirm that removing either component results in at least 10% performance degradation, validating the synergistic nature of our approach. SuS achieves 17.4% improvement in Pass@1 and 26.4% improvement in Pass@5 compared to baseline methods, while maintaining higher strategy diversity throughout training.

In collaborative learning with streaming data, nodes (e.g., organizations) jointly and continuously learn a machine learning (ML) model by sharing the latest model updates computed from their latest streaming data. For the more resourceful nodes to be willing to share their model updates, they need to be fairly incentivized. This paper explores an incentive design that guarantees fairness so that nodes receive rewards commensurate to their contributions. Our approach leverages an explore-then-exploit formulation to estimate the nodes' contributions (i.e., exploration) for realizing our theoretically guaranteed fair incentives (i.e., exploitation). However, we observe a "rich get richer" phenomenon arising from the existing approaches to guarantee fairness and it discourages the participation of the less resourceful nodes. To remedy this, we additionally preserve asymptotic equality, i.e., less resourceful nodes achieve equal performance eventually to the more resourceful/"rich" nodes. We empirically demonstrate in two settings with real-world streaming data: federated online incremental learning and federated reinforcement learning, that our proposed approach outperforms existing baselines in fairness and learning performance while remaining competitive in preserving equality.

Automated red-teaming has become a crucial approach for uncovering vulnerabilities in large language models (LLMs). However, most existing methods focus on isolated safety flaws, limiting their ability to adapt to dynamic defenses and uncover complex vulnerabilities efficiently. To address this challenge, we propose Auto-RT, a reinforcement learning framework that automatically explores and optimizes complex attack strategies to effectively uncover security vulnerabilities through malicious queries. Specifically, we introduce two key mechanisms to reduce exploration complexity and improve strategy optimization: 1) Early-terminated Exploration, which accelerate exploration by focusing on high-potential attack strategies; and 2) Progressive Reward Tracking algorithm with intermediate downgrade models, which dynamically refine the search trajectory toward successful vulnerability exploitation. Extensive experiments across diverse LLMs demonstrate that, by significantly improving exploration efficiency and automatically optimizing attack strategies, Auto-RT detects a boarder range of vulnerabilities, achieving a faster detection speed and 16.63\% higher success rates compared to existing methods.

Large Language Models (LLMs) have shown remarkable reasoning capabilities through Reinforcement Learning with Verifiable Rewards (RLVR) methods. However, a key limitation of existing approaches is that rewards defined at the full trajectory level provide insufficient guidance for optimizing the intermediate steps of a reasoning process. To address this, we introduce \name, a novel method that estimates the mathematical expectations of rewards at various reasoning steps using tree sampling. Unlike prior methods that rely on a separate step reward model, \name directly estimates these rewards through this sampling process. Building on the group-relative reward training mechanism of GRPO, \name innovatively computes rewards based on step-level groups generated during tree sampling. This advancement allows \name to produce fine-grained and dense reward signals, significantly enhancing the learning process and overall performance of LLMs. Experimental results demonstrate that our \name algorithm substantially improves the average Pass@1 accuracy of Qwen-2.5-Math on test benchmarks, increasing it from 19.0\% to 35.5\%. Furthermore, \name significantly outperforms GRPO by 2.9\% in performance while simultaneously reducing the average response length by 18.1\%, showcasing its effectiveness and efficiency. Our code will be available at https://github.com/yangzhch6/TreeRPO{https://github.com/yangzhch6/TreeRPO}.

Reinforcement Learning with Verifiable Rewards (RLVR), particularly GRPO, has become the standard for eliciting LLM reasoning. However, its efficiency in exploration and difficulty adaptation remains an open challenge. In this work, we argue that these bottlenecks stem from an implicit advantage symmetry inherent in Group Relative Advantage Estimation (GRAE). This symmetry induces two critical limitations: (i) at the group level, strict symmetry in weights between correct and incorrect trajectories leaves unsampled action logits unchanged, thereby hindering exploration of novel correct solution. (ii) at the sample level, the algorithm implicitly prioritizes medium-difficulty samples, remaining agnostic to the non-stationary demands of difficulty focus. Through controlled experiments, we reveal that this symmetric property is sub-optimal, yielding two pivotal insights: (i) asymmetrically suppressing the advantages of correct trajectories encourages essential exploration. (ii) learning efficiency is maximized by a curriculum-like transition-prioritizing simpler samples initially before gradually shifting to complex ones. Motivated by these findings, we propose Asymmetric GRAE (A-GRAE), which dynamically modulates exploration incentives and sample-difficulty focus. Experiments across seven benchmarks demonstrate that A-GRAE consistently improves GRPO and its variants across both LLMs and MLLMs.

We advance the study of incentivized bandit exploration, in which arm choices are viewed as recommendations and are required to be Bayesian incentive compatible. Recent work has shown under certain independence assumptions that after collecting enough initial samples, the popular Thompson sampling algorithm becomes incentive compatible. We give an analog of this result for linear bandits, where the independence of the prior is replaced by a natural convexity condition. This opens up the possibility of efficient and regret-optimal incentivized exploration in high-dimensional action spaces. In the semibandit model, we also improve the sample complexity for the pre-Thompson sampling phase of initial data collection.

Recent advancements have shown that reinforcement learning (RL) can substantially improve the reasoning abilities of large language models (LLMs). The effectiveness of such RL training, however, depends critically on the exploration space defined by the pre-trained model's token-output distribution. In this paper, we revisit the standard cross-entropy loss, interpreting it as a specific instance of policy gradient optimization applied within a single-step episode. To systematically study how the pre-trained distribution shapes the exploration potential for subsequent RL, we propose a generalized pre-training objective that adapts on-policy RL principles to supervised learning. By framing next-token prediction as a stochastic decision process, we introduce a reward-shaping strategy that explicitly balances diversity and precision. Our method employs a positive reward scaling factor to control probability concentration on ground-truth tokens and a rank-aware mechanism that treats high-ranking and low-ranking negative tokens asymmetrically. This allows us to reshape the pre-trained token-output distribution and investigate how to provide a more favorable exploration space for RL, ultimately enhancing end-to-end reasoning performance. Contrary to the intuition that higher distribution entropy facilitates effective exploration, we find that imposing a precision-oriented prior yields a superior exploration space for RL.

Test-time reinforcement learning (TTRL) enables large language models (LLMs) to self-improve on unlabeled inputs, but its effectiveness critically depends on how reward signals are estimated without ground-truth supervision. Most existing TTRL methods rely on majority voting (MV) over rollouts to produce deterministic rewards, implicitly assuming that the majority rollout provides a reliable learning signal. We show that this assumption is fragile: MV reduces the rollout distribution into a single outcome, discarding information about non-majority but correct actions candidates, and yields systematically biased reward estimates. To address this, we propose Distribution-AwareReward Estimation (DARE), which shifts reward estimation from a single majority outcome to the full empirical rollout distribution. DARE further augments this distribution-based reward with an exploration bonus and a distribution pruning mechanism for non-majority rollout exploration and reward denoise, yielding a more informative and robust reward estimation. Extensive experiments on challenging reasoning benchmarks show that DARE improves optimization stability and final performance over recent baselines, achieving relative improvements of 25.3% on challenging AIME 2024 and 5.3% on AMC.

Reinforcement learning algorithms such as GRPO have driven recent advances in large language model (LLM) reasoning. While scaling the number of rollouts stabilizes training, existing approaches suffer from limited exploration on challenging prompts and leave informative feedback signals underexploited, due to context-independent rollout allocation across prompts (e.g., generating 16 rollouts per prompt) and relying heavily on sparse rewards. This paper presents XRPO(eXplore - eXploit GRPO), a unified framework that recasts policy optimization through the principled lens of rollout exploration-exploitation. To enhance exploration, XRPO introduces a mathematically grounded rollout allocator that adaptively prioritizes prompts with higher potential for uncertainty reduction. It further addresses stagnation on zero-reward prompts through an in-context seeding strategy that injects curated exemplars, steering the model into more difficult reasoning trajectories. To strengthen exploitation, XRPO develops a group-relative, novelty-aware advantage sharpening mechanism that leverages sequence likelihoods to amplify low-probability yet correct responses, thereby extending the policy's reach beyond sparse rewards. Experiments across diverse math and coding benchmarks on both reasoning and non-reasoning models demonstrate that XRPO outperforms existing advances (e.g., GRPO and GSPO) up to 4% pass@1 and 6% cons@32, while accelerating training convergence by up to 2.7X.

Recent advances in large reasoning models highlight Reinforcement Learning with Verifiable Rewards (RLVR) as a promising method for enhancing AI's capabilities, particularly in solving complex logical tasks. However, it remains unclear whether RLVR truly expands a model's reasoning boundary or merely amplifies high-reward outputs that the base model already knows for improved precision. This study presents a theoretical and empirical investigation that provides fresh insights into the potential limits of RLVR. First, we offer a new theoretical perspective that RLVR is constrained by the base model's support-unable to sample solutions with zero initial probability-and operates as a conservative reweighting mechanism that may restrict the discovery of entirely original solutions. We also identify an entropy-reward tradeoff: while RLVR reliably enhances precision, it may progressively narrow exploration and potentially overlook correct yet underrepresented solutions. Extensive empirical experiments validate that while RLVR consistently improves pass@1, the shrinkage of empirical support generally outweighs the expansion of empirical support under larger sampling budgets, failing to recover correct answers that were previously accessible to the base model. Interestingly, we also observe that while RLVR sometimes increases token-level entropy, resulting in greater uncertainty at each generation step, answer-level entropy declines, indicating that these seemingly more uncertain paths ultimately converge onto a smaller set of distinct answers. Taken together, these findings reveal potential limits of RLVR in extending reasoning horizons. Breaking this invisible leash may require future algorithmic innovations such as explicit exploration mechanisms or hybrid strategies that seed probability mass into underrepresented solution regions.

Reinforcement learning is increasingly used for code-centric tasks. These tasks include code generation, summarization, understanding, repair, testing, and optimization. This trend is growing faster with large language models and autonomous agents. A key challenge is how to design reward signals that make sense for software. In many RL problems, the reward is a clear number. In software, this is often not possible. The goal is rarely a single numeric objective. Instead, rewards are usually proxies. Common proxies check if the code compiles, passes tests, or satisfies quality metrics. Many reward designs have been proposed for code-related tasks. However, the work is scattered across areas and papers. There is no single survey that brings these approaches together and shows the full landscape of reward design for RL in software. In this survey, we provide the first systematic and comprehensive review of reward engineering for RL in software tasks. We focus on existing methods and techniques. We structure the literature along three complementary dimensions, summarizing the reward-design choices within each. We conclude with challenges and recommendations in the reward design space for SE tasks.

Current critic-free RL methods for large reasoning models suffer from severe inefficiency when training on positive homogeneous prompts (where all rollouts are correct), resulting in waste of rollouts due to zero advantage estimates. We introduce a radically simple yet powerful solution to Mine intrinsic mastery (Miner), that repurposes the policy's intrinsic uncertainty as a self-supervised reward signal, with no external supervision, auxiliary models, or additional inference cost. Our method pioneers two key innovations: (1) a token-level focal credit assignment mechanism that dynamically amplifies gradients on critical uncertain tokens while suppressing overconfident ones, and (2) adaptive advantage calibration to seamlessly integrate intrinsic and verifiable rewards. Evaluated across six reasoning benchmarks on Qwen3-4B and Qwen3-8B base models, Miner achieves state-of-the-art performance among the other four algorithms, yielding up to 4.58 absolute gains in Pass@1 and 6.66 gains in Pass@K compared to GRPO. Comparison with other methods targeted at exploration enhancement further discloses the superiority of the two newly proposed innovations. This demonstrates that latent uncertainty exploitation is both necessary and sufficient for efficient and scalable RL training of reasoning models.

Learning optimal policies in sparse rewards settings is difficult as the learning agent has little to no feedback on the quality of its actions. In these situations, a good strategy is to focus on exploration, hopefully leading to the discovery of a reward signal to improve on. A learning algorithm capable of dealing with this kind of settings has to be able to (1) explore possible agent behaviors and (2) exploit any possible discovered reward. Efficient exploration algorithms have been proposed that require to define a behavior space, that associates to an agent its resulting behavior in a space that is known to be worth exploring. The need to define this space is a limitation of these algorithms. In this work, we introduce STAX, an algorithm designed to learn a behavior space on-the-fly and to explore it while efficiently optimizing any reward discovered. It does so by separating the exploration and learning of the behavior space from the exploitation of the reward through an alternating two-steps process. In the first step, STAX builds a repertoire of diverse policies while learning a low-dimensional representation of the high-dimensional observations generated during the policies evaluation. In the exploitation step, emitters are used to optimize the performance of the discovered rewarding solutions. Experiments conducted on three different sparse reward environments show that STAX performs comparably to existing baselines while requiring much less prior information about the task as it autonomously builds the behavior space.

We introduce Robust Exploration via Clustering-based Online Density Estimation (RECODE), a non-parametric method for novelty-based exploration that estimates visitation counts for clusters of states based on their similarity in a chosen embedding space. By adapting classical clustering to the nonstationary setting of Deep RL, RECODE can efficiently track state visitation counts over thousands of episodes. We further propose a novel generalization of the inverse dynamics loss, which leverages masked transformer architectures for multi-step prediction; which in conjunction with RECODE achieves a new state-of-the-art in a suite of challenging 3D-exploration tasks in DM-Hard-8. RECODE also sets new state-of-the-art in hard exploration Atari games, and is the first agent to reach the end screen in "Pitfall!".

In open-ended environments, exploration is fundamental for autonomous agents, yet current language model agents struggle with this. Effective exploration requires memory, but retaining raw interaction histories is computationally expensive over long trajectories. While latent memory offers a solution to compress interaction histories, its training lacks reliable supervisory signals. We introduce Joint Agent Memory and Exploration Learning (JAMEL), a framework that trains agentic memory and exploration policy together through novelty-driven interaction. We observe that memory and exploration form a mutually dependent loop: sustained exploration requires memory to distinguish exhausted behaviors from unseen ones, while novelty-seeking interaction provides the supervision needed to make memory useful for future exploration. By utilizing deterministic and persistent novelty signals such as code coverage in the GUI domain, we provide natural, annotation-free supervision for the memory module. Empirical evaluations demonstrate that \ours successfully generalizes to unseen environments. Its exploration capability outperforms open-weight baselines and rivals the exploration depth of a closed-source model while reducing token consumption. Our code and model are open-sourced at https://github.com/MobileLLM/JAMEL.

Large reasoning models (LRMs) have recently shown promise in solving complex math problems when optimized with Reinforcement Learning (RL). But conventional approaches rely on outcome-only rewards that provide sparse feedback, resulting in inefficient optimization process. In this work, we investigate the function of process reward models (PRMs) to accelerate the RL training for LRMs. We propose a novel intrinsic signal-driven generative process evaluation mechanism operating at the thought level to address major bottlenecks in RL-based training. Specifically, instead of requiring PRMs to know how to solve problems, our method uses intrinsic signals in solutions to judge stepwise correctness and aggregate contiguous correct/incorrect steps into coherent 'thought' units. This structured, thought-level rewards enable more reliable credit assignment by reducing ambiguity in step segmentation and alleviating reward hacking. We further introduce a capability-adaptive reward mechanism that dynamically balances exploration and exploitation based on the LRM's current proficiency, guiding learning without stifling creative trial-and-error. These innovations are integrated into a new off-policy RL algorithm, TP-GRPO, which extends grouped proximal optimization with process-based rewards and improves training efficiency. Experiments on 1.5B and 7B parameter LRMs demonstrate that our method achieves higher problem-solving accuracy with significantly fewer training samples than outcome-only reward baselines. The results validate that well-structured process rewards can substantially accelerate LRM optimization in math reasoning tasks. Code is available at https://github.com/cs-holder/tp_grpo.

Complex numerical time series analysis often demands multi-step reasoning capabilities beyond current models' reach. Tasks like medical diagnosis and weather forecasting require sequential reasoning processes - including counterfactual analysis, logical deduction, knowledge application, and multi-modal contextual integration - that existing time series models cannot explicitly perform. While recent research has shown large language models (LLMs) can achieve sophisticated Chain-of-Thought (CoT) reasoning through reinforcement learning (RL), these advances have primarily focused on mathematical and coding domains, with LLMs still demonstrating poor performance on time series tasks. We introduce Chain Of thought for Understanding Numerical Time Series (COUNTS), the first framework that trains LLMs to perform CoT reasoning across diverse time series tasks using RL with verifiable rewards. Our approach employs a Residual Vector-Quantized VAE to create high-fidelity discrete tokens that seamlessly integrate into a pre-trained LLM's vocabulary. COUNTS undergoes a two-stage training process: first, supervised fine-tuning on time series analysis tasks to master our novel representations, followed by Group Relative Policy Optimization training on verifiable problems using prompting strategies that encourage explicit reasoning steps before producing final answers. Our experiments demonstrate that this RL-driven approach with intermediate CoT reasoning significantly enhances LLM performance across various time series analysis tasks, opening new possibilities for complex temporal data reasoning.

Reinforcement learning with verifiable rewards (RLVR) is effective for training large language models on deterministic outcome reasoning tasks. Prior work shows RLVR works with few prompts, but prompt selection is often based only on training-accuracy variance, leading to unstable optimization directions and weaker transfer. We revisit prompt selection from a mechanism-level view and argue that an effective minibatch should provide both (i) a reliable positive anchor and (ii) explicit negative learning signals from rare failures. Based on this principle, we propose positive--negative pairing: at each update, we sample a hard-but-solvable q^{+} and an easy-but-brittle prompt q^{-}(high success rate but not perfect), characterized by low and high empirical success rates under multiple rollouts. We further introduce Weighted GRPO, which reweights binary outcomes at the pair level and uses group-normalized advantages to amplify rare successes on q^{+} into sharp positive guidance while turning rare failures on q^{-} into strong negative penalties. This bidirectional signal provides informative learning feedback for both successes and failures, improving sample efficiency without suppressing exploration. On Qwen2.5-Math-7B, a single paired minibatch per update consistently outperforms a GRPO baseline that selects two prompts via commonly used variance-based selection heuristics: AIME~2025 Pass@8 improves from 16.8 to 22.2, and AMC23 Pass@64 from 94.0 to 97.0, while remaining competitive with large-scale RLVR trained from a pool of 1209 training prompts. Similar gains are observed on Qwen2.5-Math-7B-Instruct.

Recent advances in Reinforcement Learning with Verifiable Rewards (RLVR) for Large Language Model (LLM) reasoning have been hindered by a persistent challenge: exploration collapse. The semantic homogeneity of random rollouts often traps models in narrow, over-optimized behaviors. While existing methods leverage policy entropy to encourage exploration, they face inherent limitations. Global entropy regularization is susceptible to reward hacking, which can induce meaningless verbosity, whereas local token-selective updates struggle with the strong inductive bias of pre-trained models. To address this, we propose Latent Policy Optimization via Iterative Information Bottleneck (IIB-LPO), a novel approach that shifts exploration from statistical perturbation of token distributions to topological branching of reasoning trajectories. IIB-LPO triggers latent branching at high-entropy states to diversify reasoning paths and employs the Information Bottleneck principle both as a trajectory filter and a self-reward mechanism, ensuring concise and informative exploration. Empirical results across four mathematical reasoning benchmarks demonstrate that IIB-LPO achieves state-of-the-art performance, surpassing prior methods by margins of up to 5.3% in accuracy and 7.4% in diversity metrics.

Text-to-SQL is a challenging task involving multiple reasoning-intensive subtasks, including natural language understanding, database schema comprehension, and precise SQL query formulation. Existing approaches often rely on handcrafted reasoning paths with inductive biases that can limit their overall effectiveness. Motivated by the recent success of reasoning-enhanced models such as DeepSeek R1 and OpenAI o1, which effectively leverage reward-driven self-exploration to enhance reasoning capabilities and generalization, we propose a novel set of partial rewards tailored specifically for the Text-to-SQL task. Our reward set includes schema-linking, AI feedback, n-gram similarity, and syntax check, explicitly designed to address the reward sparsity issue prevalent in reinforcement learning (RL). Leveraging group relative policy optimization (GRPO), our approach explicitly encourages large language models (LLMs) to develop intrinsic reasoning skills necessary for accurate SQL query generation. With models of different sizes, we demonstrate that RL-only training with our proposed rewards consistently achieves higher accuracy and superior generalization compared to supervised fine-tuning (SFT). Remarkably, our RL-trained 14B-parameter model significantly outperforms larger proprietary models, e.g. o3-mini by 4% and Gemini-1.5-Pro-002 by 3% on the BIRD benchmark. These highlight the efficacy of our proposed RL-training framework with partial rewards for enhancing both accuracy and reasoning capabilities in Text-to-SQL tasks.

Local prediction-error-based curiosity rewards focus on the current transition without considering the world model's cumulative prediction error across all visited transitions. We introduce Curiosity-Critic, which grounds its intrinsic reward in the improvement of this cumulative objective, and show that it reduces to a tractable per-step form: the difference between the current prediction error and the asymptotic error baseline of the current state transition. We estimate this baseline online with a learned critic co-trained alongside the world model; regressing a single scalar, the critic converges well before the world model saturates, redirecting exploration toward learnable transitions without oracle knowledge of the noise floor. The reward is higher for learnable transitions and collapses toward the baseline for stochastic ones, effectively separating epistemic (reducible) from aleatoric (irreducible) prediction error online. Prior prediction-error curiosity formulations, from Schmidhuber (1991) to learned-feature-space variants, emerge as special cases corresponding to specific approximations of this baseline. Experiments on a stochastic grid world show that Curiosity-Critic outperforms prediction-error and visitation-count baselines in convergence speed and final world model accuracy.

Reinforcement learning drives recent advances in LLM reasoning and agentic capabilities, yet current approaches struggle with both exploration and exploitation. Exploration suffers from low success rates on difficult tasks and high costs of repeated rollouts from scratch. Exploitation suffers from coarse credit assignment and training instability: Trajectory-level rewards penalize valid prefixes for later errors, and failure-dominated groups overwhelm the few positive signals, leaving optimization without constructive direction. To this end, we propose R^3L, Reflect-then-Retry Reinforcement Learning with Language-Guided Exploration, Pivotal Credit, and Positive Amplification. To synthesize high-quality trajectories, R^3L shifts from stochastic sampling to active synthesis via reflect-then-retry, leveraging language feedback to diagnose errors, transform failed attempts into successful ones, and reduce rollout costs by restarting from identified failure points. With errors diagnosed and localized, Pivotal Credit Assignment updates only the diverging suffix where contrastive signals exist, excluding the shared prefix from gradient update. Since failures dominate on difficult tasks and reflect-then-retry produces off-policy data, risking training instability, Positive Amplification upweights successful trajectories to ensure positive signals guide the optimization process. Experiments on agentic and reasoning tasks demonstrate 5\% to 52\% relative improvements over baselines while maintaining training stability. Our code is released at https://github.com/shiweijiezero/R3L.

Generative recommendation via autoregressive models has unified retrieval and ranking into a single conditional generation framework. However, fine-tuning these models with Reinforcement Learning (RL) often suffers from a fundamental probability-reward mismatch. Conventional likelihood-dominated decoding (e.g., beam search) exhibits a myopic bias toward locally probable prefixes, which causes two critical failures: (1) insufficient exploration, where high-reward items in low-probability branches are prematurely pruned and rarely sampled, and (2) advantage compression, where trajectories sharing high-probability prefixes receive highly correlated rewards with low within-group variance, yielding a weak comparative signal for RL. To address these challenges, we propose V-STAR, a Value-guided Sampling and Tree-structured Advantage Reinforcement framework. V-STAR forms a self-evolving loop via two synergistic components. First, a Value-Guided Efficient Decoding (VED) is developed to identify decisive nodes and selectively deepen high-potential prefixes. This improves exploration efficiency without exhaustive tree search. Second, we propose Sibling-GRPO, which exploits the induced tree topology to compute sibling-relative advantages and concentrates learning signals on decisive branching decisions. Extensive experiments on both offline and online datasets demonstrate that V-STAR outperforms state-of-the-art baselines, delivering superior accuracy and candidate-set diversity under strict latency constraints.

Reinforcement learning (RL) is the dominant paradigm for sharpening strategic tool use capabilities of LLMs on long-horizon, sparsely-rewarded agent tasks, yet it faces a fundamental challenge of exploration-exploitation trade-off. Existing studies stimulate exploration through the lens of policy entropy, but such mechanical entropy maximization is prone to RL training instability due to the multi-turn distribution shifting. In this paper, we target the progressive exploration-exploitation balance under the guidance of the agent own experiences without succumbing to either entropy collapsing or runaway divergence. We propose SPEAR, a curriculum-based self-imitation learning (SIL) recipe for training agentic LLMs. It extends the vanilla SIL framework, where a replay buffer stores self-generated promising trajectories for off-policy update, by gradually steering the policy evolution within a well-balanced range of entropy across stages. Specifically, our approach incorporates a curriculum to manage the exploration process, utilizing intrinsic rewards to foster skill-level exploration and facilitating action-level exploration through SIL. At first, the auxiliary tool call reward plays a critical role in the accumulation of tool-use skills, enabling broad exposure to the unfamiliar distributions of the environment feedback with an upward entropy trend. As training progresses, self-imitation gets strengthened to exploit existing successful patterns from replayed experiences for comparative action-level exploration, accelerating solution iteration without unbounded entropy growth. To further stabilize training, we recalibrate the advantages of experiences in the replay buffer to address the potential policy drift. Reugularizations such as the clipping of tokens with high covariance between probability and advantage are introduced to the trajectory-level entropy control to curb over-confidence.

Visual reinforcement learning (RL) has shown promise in continuous control tasks. Despite its progress, current algorithms are still unsatisfactory in virtually every aspect of the performance such as sample efficiency, asymptotic performance, and their robustness to the choice of random seeds. In this paper, we identify a major shortcoming in existing visual RL methods that is the agents often exhibit sustained inactivity during early training, thereby limiting their ability to explore effectively. Expanding upon this crucial observation, we additionally unveil a significant correlation between the agents' inclination towards motorically inactive exploration and the absence of neuronal activity within their policy networks. To quantify this inactivity, we adopt dormant ratio as a metric to measure inactivity in the RL agent's network. Empirically, we also recognize that the dormant ratio can act as a standalone indicator of an agent's activity level, regardless of the received reward signals. Leveraging the aforementioned insights, we introduce DrM, a method that uses three core mechanisms to guide agents' exploration-exploitation trade-offs by actively minimizing the dormant ratio. Experiments demonstrate that DrM achieves significant improvements in sample efficiency and asymptotic performance with no broken seeds (76 seeds in total) across three continuous control benchmark environments, including DeepMind Control Suite, MetaWorld, and Adroit. Most importantly, DrM is the first model-free algorithm that consistently solves tasks in both the Dog and Manipulator domains from the DeepMind Control Suite as well as three dexterous hand manipulation tasks without demonstrations in Adroit, all based on pixel observations.

Large language models have achieved strong performance on medical reasoning benchmarks, yet their deployment in clinical settings demands rigorous verification to ensure factual accuracy. While reward models offer a scalable approach for reasoning trace verification, existing methods face two limitations: they produce only scalar reward values without explicit justification, and they rely on single-pass retrieval that precludes adaptive knowledge access as verification unfolds. We introduce method, an agentic framework that addresses these limitations by training medical reasoning verifiers to iteratively query external medical corpora during evaluation. Our approach combines tool-augmented verification with an iterative reinforcement learning paradigm that requires only trace-level supervision, alongside an adaptive curriculum mechanism that dynamically adjusts training data distribution. Across four medical reasoning benchmarks, method achieves substantial gains over existing methods, improving MedQA accuracy by 23.5% and MedXpertQA by 32.0% relative to the base generator in particular. Crucially, method demonstrates an 8times reduction in sampling budget requirement compared to prior reward model baselines. These findings establish that grounding verification in dynamically retrieved evidence offers a principled path toward more reliable medical reasoning systems.

Reinforcement learning (RL) has emerged as a critical technique for enhancing LLM-based deep search agents. However, existing approaches primarily rely on binary outcome rewards, which fail to capture the comprehensiveness and factuality of agents' reasoning process, and often lead to undesirable behaviors such as shortcut exploitation and hallucinations. To address these limitations, we propose Citation-aware Rubric Rewards (CaRR), a fine-grained reward framework for deep search agents that emphasizes reasoning comprehensiveness, factual grounding, and evidence connectivity. CaRR decomposes complex questions into verifiable single-hop rubrics and requires agents to satisfy these rubrics by explicitly identifying hidden entities, supporting them with correct citations, and constructing complete evidence chains that link to the predicted answer. We further introduce Citation-aware Group Relative Policy Optimization (C-GRPO), which combines CaRR and outcome rewards for training robust deep search agents. Experiments show that C-GRPO consistently outperforms standard outcome-based RL baselines across multiple deep search benchmarks. Our analysis also validates that C-GRPO effectively discourages shortcut exploitation, promotes comprehensive, evidence-grounded reasoning, and exhibits strong generalization to open-ended deep research tasks. Our code and data are available at https://github.com/THUDM/CaRR.

Conventional Applicant Tracking Systems (ATS) tend to be inflexible keyword-matchers, and deny gifted candidates a role due to a few minor semantic mismatches. This article describes a new two-step process to design a more refined resume evaluation model based on a small language model (<600M parameters) that is finetuned using GRPO on a custom reward function. To begin with, Supervised Fine-Tuning (SFT) was used to build a solid baseline model. Second, this SFT model was also optimized with the help of Reinforcement Learning (RL) through GRPO under the guidance of a new, multi-component reward function that can holistically assess candidates beyond simple keyword matching. We indicate that the RL application presents a critical problem of reward hacking due to the initial experiments of aggressive penalties, which produces faulty, excessively negative model behaviors. We have overcome this challenge by refining the reward function repeatedly and training hyperparameters into a stable "gentle polishing process" of the reward function. Our resulting GRPO-polished model demonstrates significant real-world efficacy, achieving a final accuracy of 91% on unseen test data. The model shows a strong ability to correctly identify qualified candidates (recall of 0.85 for the 'SELECTED' class) while also showing exceptional precision (1.0), confirming its reliability. These results indicate that a properly executed, two-step fine-tuning procedure can indeed effectively refine a small language model to be able to conduct fine-tuned and human-like candidate scoring, overcoming the drawbacks of both traditional ATS and naive RL usage.

Entropy regularization is a standard technique in reinforcement learning (RL) to enhance exploration, yet it yields negligible effects or even degrades performance in Large Language Models (LLMs). We attribute this failure to the cumulative tail risk inherent to LLMs with massive vocabularies and long generation horizons. In such environments, standard global entropy maximization indiscriminately dilutes probability mass into the vast tail of invalid tokens rather than focusing on plausible candidates, thereby disrupting coherent reasoning. To address this, we propose Trust Region Entropy (TRE), a method that encourages exploration strictly within the model's trust region. Extensive experiments across mathematical reasoning (MATH), combinatorial search (Countdown), and preference alignment (HH) tasks demonstrate that TRE consistently outperforms vanilla PPO, standard entropy regularization, and other exploration baselines. Our code is available at https://github.com/WhyChaos/TRE-Encouraging-Exploration-in-the-Trust-Region.

Large Language Models (LLMs) can self-improve through reinforcement learning, where they generate trajectories to explore and discover better solutions. However, this exploration process is computationally expensive, often forcing current methods to assign limited exploration budgets to each task. This uniform allocation creates problematic edge cases: easy tasks consistently succeed while difficult tasks consistently fail, both producing zero gradients during training updates for the widely used Group Relative Policy Optimization (GRPO). We address this problem from the lens of exploration budget allocation. Viewing each task's exploration as an "item" with a distinct "value" and "cost", we establish a connection to the classical knapsack problem. This formulation allows us to derive an optimal assignment rule that adaptively distributes resources based on the model's current learning status. When applied to GRPO, our method increases the effective ratio of non-zero policy gradients by 20-40% during training. Acting as a computational "free lunch", our approach could reallocate exploration budgets from tasks where learning is saturated to those where it is most impactful. This enables significantly larger budgets (e.g., 93 rollouts) for especially challenging problems, which would be computationally prohibitive under a uniform allocation. These improvements translate to meaningful gains on mathematical reasoning benchmarks, with average improvements of 2-4 points and peak gains of 9 points on specific tasks. Notably, achieving comparable performance with traditional homogeneous allocation would require about 2x the computational resources.

Large language models for mathematical reasoning are typically trained with outcome-based rewards, which credit only the final answer. In our experiments, we observe that this paradigm is highly susceptible to reward hacking, leading to a substantial overestimation of a model's reasoning ability. This is evidenced by a high incidence of false positives - solutions that reach the correct final answer through an unsound reasoning process. Through a systematic analysis with human verification, we establish a taxonomy of these failure modes, identifying patterns like Miracle Steps - abrupt jumps to a correct output without a valid preceding derivation. Probing experiments suggest a strong association between these Miracle Steps and memorization, where the model appears to recall the answer directly rather than deriving it. To mitigate this systemic issue, we introduce the Rubric Reward Model (RRM), a process-oriented reward function that evaluates the entire reasoning trajectory against problem-specific rubrics. The generative RRM provides fine-grained, calibrated rewards (0-1) that explicitly penalize logical flaws and encourage rigorous deduction. When integrated into a reinforcement learning pipeline, RRM-based training consistently outperforms outcome-only supervision across four math benchmarks. Notably, it boosts Verified Pass@1024 on AIME2024 from 26.7% to 62.6% and reduces the incidence of Miracle Steps by 71%. Our work demonstrates that rewarding the solution process is crucial for building models that are not only more accurate but also more reliable.

We propose FlowRL: matching the full reward distribution via flow balancing instead of maximizing rewards in large language model (LLM) reinforcement learning (RL). Recent advanced reasoning models adopt reward-maximizing methods (\eg, PPO and GRPO), which tend to over-optimize dominant reward signals while neglecting less frequent but valid reasoning paths, thus reducing diversity. In contrast, we transform scalar rewards into a normalized target distribution using a learnable partition function, and then minimize the reverse KL divergence between the policy and the target distribution. We implement this idea as a flow-balanced optimization method that promotes diverse exploration and generalizable reasoning trajectories. We conduct experiments on math and code reasoning tasks: FlowRL achieves a significant average improvement of 10.0% over GRPO and 5.1% over PPO on math benchmarks, and performs consistently better on code reasoning tasks. These results highlight reward distribution-matching as a key step toward efficient exploration and diverse reasoning in LLM reinforcement learning.

In this work, we study the issue of reward hacking on the response length, a challenge emerging in Reinforcement Learning from Human Feedback (RLHF) on LLMs. A well-formatted, verbose but less helpful response from the LLMs can often deceive LLMs or even human evaluators to achieve high scores. The same issue also holds for some reward models in RL. To address the challenges in both training and evaluation, we establish a more reliable evaluation protocol for comparing different training configurations, which inspects the trade-off between LLM evaluation score and response length obtained by varying training hyperparameters. Based on this evaluation, we conduct large-scale studies, where the results shed insights into the efficacy of hyperparameters and tricks used in RL on mitigating length bias. We further propose to improve the reward model by jointly training two linear heads on shared feature representations to predict the rewards, one trained to correlate with length, and the other trained to decorrelate with length and therefore focus more on the actual content. We then discard the length head in RL to prevent reward hacking on length. Experiments demonstrate that our approach almost eliminates the reward correlation with length, and improves the obtained policy by a significant margin.

Reward-guided search methods have demonstrated strong potential in enhancing tool-using agents by effectively guiding sampling and exploration over complex action spaces. As a core design, those search methods utilize process reward models (PRMs) to provide step-level rewards, enabling more fine-grained monitoring. However, there is a lack of systematic and reliable evaluation benchmarks for PRMs in tool-using settings. In this paper, we introduce ToolPRMBench, a large-scale benchmark specifically designed to evaluate PRMs for tool-using agents. ToolPRMBench is built on top of several representative tool-using benchmarks and converts agent trajectories into step-level test cases. Each case contains the interaction history, a correct action, a plausible but incorrect alternative, and relevant tool metadata. We respectively utilize offline sampling to isolate local single-step errors and online sampling to capture realistic multi-step failures from full agent rollouts. A multi-LLM verification pipeline is proposed to reduce label noise and ensure data quality. We conduct extensive experiments across large language models, general PRMs, and tool-specialized PRMs on ToolPRMBench. The results reveal clear differences in PRM effectiveness and highlight the potential of specialized PRMs for tool-using. Code and data will be released at https://github.com/David-Li0406/ToolPRMBench.

Sampling is ubiquitous in machine learning methodologies. Due to the growth of large datasets and model complexity, we want to learn and adapt the sampling process while training a representation. Towards achieving this grand goal, a variety of sampling techniques have been proposed. However, most of them either use a fixed sampling scheme or adjust the sampling scheme based on simple heuristics. They cannot choose the best sample for model training in different stages. Inspired by "Think, Fast and Slow" (System 1 and System 2) in cognitive science, we propose a reward-guided sampling strategy called Adaptive Sample with Reward (ASR) to tackle this challenge. To the best of our knowledge, this is the first work utilizing reinforcement learning (RL) to address the sampling problem in representation learning. Our approach optimally adjusts the sampling process to achieve optimal performance. We explore geographical relationships among samples by distance-based sampling to maximize overall cumulative reward. We apply ASR to the long-standing sampling problems in similarity-based loss functions. Empirical results in information retrieval and clustering demonstrate ASR's superb performance across different datasets. We also discuss an engrossing phenomenon which we name as "ASR gravity well" in experiments.

Reinforcement learning with verifiable rewards (RLVR) is a powerful paradigm for enhancing the reasoning capabilities of large language models (LLMs), yet its success hinges on effective exploration. An ideal exploration strategy must navigate two fundamental challenges: it must preserve sample quality while also ensuring training stability. While standard fixed-temperature sampling is simple, it struggles to balance these competing demands, as high temperatures degrade sample quality and low temperatures limit discovery. In this work, we propose a simpler and more effective strategy, Exploratory Annealed Decoding (EAD), grounded in the insight that exploration is most impactful on early tokens which define a sequence's semantic direction. EAD implements an intuitive **explore-at-the-beginning, exploit-at-the-end** strategy by annealing the sampling temperature from high to low during generation. This dynamic schedule encourages meaningful, high-level diversity at the start, then gradually lowers the temperature to preserve sample quality and keep the sampling distribution close to the target policy, which is essential for stable training. We demonstrate that EAD is a lightweight, plug-and-play method that significantly improves sample efficiency, consistently outperforming fixed-temperature sampling across various RLVR algorithms and model sizes. Our work suggests that aligning exploration with the natural dynamics of sequential generation offers a robust path to improving LLM reasoning.

Multimodal large language models (MLLMs) have shown strong capabilities in perception, reasoning, and action generation. However, their ability to sustain exploration in dynamic open worlds remains unclear. Existing embodied and game-based benchmarks often compress interaction into short-horizon tasks or entangle success with domain-specific game mechanics. In this paper, we introduce MineExplorer benchmark for evaluating open-world exploration capabilities of MLLM agents in Minecraft. We first filter atomic tasks whose solutions rely heavily on Minecraft-specific knowledge to better reflect general open-world reasoning. Then we organize the benchmark around a ReAct-style capability formulation and compose atomic tasks into implicit multi-hop tasks. To further construct reliable instances, MineExplorer uses a multi-agent synthesis workflow that jointly designs task graphs, sandbox scenes, and rule-based milestone evaluators. Human evaluation shows that the multi-agent synthesis workflow produces significantly more reliable instances than a single-agent baseline. Experiments with advanced MLLM agents show that open-world exploration remains challenging, as strong models can handle many single-hop tasks but degrade sharply when hidden prerequisites must be coordinated over longer trajectories. Further analysis finds that task difficulty tracks agent completion, and larger models or thinking modes do not consistently translate into better performance. Code and dataset are available at https://github.com/Jometeorie/MineExplorer.

We introduce T-Rex, an interactive object counting model designed to first detect and then count any objects. We formulate object counting as an open-set object detection task with the integration of visual prompts. Users can specify the objects of interest by marking points or boxes on a reference image, and T-Rex then detects all objects with a similar pattern. Guided by the visual feedback from T-Rex, users can also interactively refine the counting results by prompting on missing or falsely-detected objects. T-Rex has achieved state-of-the-art performance on several class-agnostic counting benchmarks. To further exploit its potential, we established a new counting benchmark encompassing diverse scenarios and challenges. Both quantitative and qualitative results show that T-Rex possesses exceptional zero-shot counting capabilities. We also present various practical application scenarios for T-Rex, illustrating its potential in the realm of visual prompting.

Training large language models to reason with search engines via reinforcement learning is hindered by a fundamental credit assignment problem: existing methods such as Search-R1 provide only a sparse outcome reward after an entire multi-step trajectory, making it infeasible to attribute success or failure to individual reasoning and retrieval decisions. Process-reward methods like StepSearch alleviate this by introducing step-level supervision, but rely on heuristic rewards such as TF-IDF overlap with gold documents, and still sample k complete trajectories per example, retaining high gradient variance. We propose SLATE, a framework built on two complementary ideas: (1) truncated step-level sampling, which generates k trajectories that share a common prefix and differ only at the next step, and (2) dense LLM-as-judge rewards, which replace heuristic scoring with a capable LLM evaluator that assesses the quality of each reasoning step, search query, and answer, providing richer and more reliable supervision. We theoretically prove that under the same dense reward structure, truncated sampling reduces the variance of advantage estimates by up to a factor of T compared to full-trajectory sampling for T-step trajectories, yielding lower-variance, better-targeted policy gradients. Experiments on seven QA benchmarks confirm that SLATE consistently outperforms both sparse-reward and process-reward baselines, with the largest gains on harder multi-hop tasks and smaller models.

Extrinsic rewards can effectively guide reinforcement learning (RL) agents in specific tasks. However, extrinsic rewards frequently fall short in complex environments due to the significant human effort needed for their design and annotation. This limitation underscores the necessity for intrinsic rewards, which offer auxiliary and dense signals and can enable agents to learn in an unsupervised manner. Although various intrinsic reward formulations have been proposed, their implementation and optimization details are insufficiently explored and lack standardization, thereby hindering research progress. To address this gap, we introduce RLeXplore, a unified, highly modularized, and plug-and-play framework offering reliable implementations of eight state-of-the-art intrinsic reward methods. Furthermore, we conduct an in-depth study that identifies critical implementation details and establishes well-justified standard practices in intrinsically-motivated RL. Our documentation, examples, and source code are available at https://github.com/RLE-Foundation/RLeXplore.

Open-world object counting remains brittle: despite rapid advances in vision-language models (VLMs), reliably counting the objects a user intends is far from solved. We argue that a central reason is that counting granularity is left implicit; users may refer to a specific identity, an attribute, an instance type, a category, or an abstract concept, yet most methods treat "what to count" as a single, category-level matching problem. In this work, we redefine open-world counting as multi-grained counting, where visual exemplars specify target appearance and fine-grained text, with optional negative prompts, specifies the intended semantic granularity across five explicit levels. Making granularity explicit, however, exposes a critical data bottleneck: existing counting datasets lack the multi-category scenes, controlled distractors, and instance-level annotations needed to verify fine-grained prompt semantics. To address this, we propose the first fully automatic data-scaling pipeline that integrates controllable 3D synthesis with consistent image editing and VLM-based filtering, and use it to construct KubriCount, the largest and most comprehensively annotated counting dataset to date, supporting both training and multi-grained evaluation. Systematic benchmarking reveals that both multimodal large language models and specialist counting models exhibit severe prompt-following failures under fine-grained distinctions. Motivated by these findings, we train HieraCount, a multi-grained counting model that jointly leverages text and visual exemplars as complementary target specifications. HieraCount substantially improves multi-grained counting accuracy and generalizes robustly to challenging real-world scenarios. The project page is available here: https://verg-avesta.github.io/KubriCount/.

This paper presents an advanced mathematical problem-solving framework, LLaMA-Berry, for enhancing the mathematical reasoning ability of Large Language Models (LLMs). The framework combines Monte Carlo Tree Search (MCTS) with iterative Self-Refine to optimize the reasoning path and utilizes a pairwise reward model to evaluate different paths globally. By leveraging the self-critic and rewriting capabilities of LLMs, Self-Refine applied to MCTS (SR-MCTS) overcomes the inefficiencies and limitations of conventional step-wise and greedy search algorithms by fostering a more efficient exploration of solution spaces. Pairwise Preference Reward Model~(PPRM), inspired by Reinforcement Learning from Human Feedback (RLHF), is then used to model pairwise preferences between solutions, utilizing an Enhanced Borda Count (EBC) method to synthesize these preferences into a global ranking score to find better answers. This approach addresses the challenges of scoring variability and non-independent distributions in mathematical reasoning tasks. The framework has been tested on general and advanced benchmarks, showing superior performance in terms of search efficiency and problem-solving capability compared to existing methods like ToT and rStar, particularly in complex Olympiad-level benchmarks, including GPQA, AIME24 and AMC23.

The goal of this paper is to improve the generality and accuracy of open-vocabulary object counting in images. To improve the generality, we repurpose an open-vocabulary detection foundation model (GroundingDINO) for the counting task, and also extend its capabilities by introducing modules to enable specifying the target object to count by visual exemplars. In turn, these new capabilities - being able to specify the target object by multi-modalites (text and exemplars) - lead to an improvement in counting accuracy. We make three contributions: First, we introduce the first open-world counting model, CountGD, where the prompt can be specified by a text description or visual exemplars or both; Second, we show that the performance of the model significantly improves the state of the art on multiple counting benchmarks - when using text only, CountGD is comparable to or outperforms all previous text-only works, and when using both text and visual exemplars, we outperform all previous models; Third, we carry out a preliminary study into different interactions between the text and visual exemplar prompts, including the cases where they reinforce each other and where one restricts the other. The code and an app to test the model are available at https://www.robots.ox.ac.uk/~vgg/research/countgd/.

Reinforcement learning with verifiable rewards (RLVR) has become a leading paradigm for improving the reasoning ability of large language models through outcome-based supervision. However, verifiable rewards frequently become uninformative at the group level: when all sampled traces of a given prompt receive identical rewards, group-relative advantage estimation provides no gradient signal, even though the traces may differ substantially in reasoning quality. We propose Reasoning Arena, an adaptive training framework that routes such non-diverse reward groups to a judge system instead of discarding them. Beyond examining the final answer, Reasoning Arena constructs trace tournaments, where reasoning traces are compared head-to-head to expose finer-grained preferences within the group, converting reasoning quality into rich relative reward signals. To make reward estimation efficient, rather than exhaustively comparing every pair, each new trace is evaluated against a small, dynamically updated pool of previously generated traces as anchors to efficiently establish a relative ranking. We then fit a Bradley-Terry model on the incomplete comparison graph, enabling scalable RL integration without quadratic pairwise comparisons. Empirical results demonstrate that Reasoning Arena consistently outperforms the RLVR baseline by 7.6% on average in competition mathematics and coding benchmarks. By converting otherwise wasted zero-advantage samples into useful gradient updates, our method accelerates training by 27% to 41%, saving nearly 50% of generation compute, and substantially improves overall reasoning performance.

Recent advances in large language models have been driven by reinforcement learning (RL)-style post-training, which improves reasoning by optimizing model outputs based on reward or preference signals. GRPO-style approaches implement this by using self-generated samples labeled by an outcome-based verifier. However, these methods depend heavily on the model's initial ability to produce positive samples. They primarily refine what the model already knows (distribution sharpening) rather than enabling the model to solve problems where it initially fails. This limitation is especially problematic in early-stage RL training and on challenging reasoning tasks, where positive samples are unlikely to be generated. To unlock reasoning ability in such settings, the model must explore new reasoning trajectories beyond its current output distribution. Such exploration requires access to sufficiently good positive samples to guide the learning. While expert demonstrations seem like a natural solution, we find that they are often ineffective in RL post-training. Instead, we identify two key properties of effective positive samples: they should (1) be likely under the current policy, and (2) increase the model's likelihood of predicting the correct answer. Based on these insights, we propose Self-Explanation Policy Optimization (ExPO)-a simple and modular framework that generates such samples by conditioning on the ground-truth answer. ExPO enables efficient exploration and guides the model to produce reasoning trajectories more aligned with its policy than expert-written CoTs, while ensuring higher quality than its own (incorrect) samples. Experiments show that ExPO improves both learning efficiency and final performance on reasoning benchmarks, surpassing expert-demonstration-based methods in challenging settings such as MATH level-5, where the model initially struggles the most.