Reinforcement Learning with Verifiable Rewards (RLVR) has propelled Large Language Models in complex reasoning, yet its scalability is often hindered by a training bottleneck where performance plateaus as policy entropy collapses, signaling a loss of exploration. Previous methods typically address this by maintaining high policy entropy, yet the precise mechanisms that govern meaningful exploration have remained underexplored. Our analysis suggests that an unselective focus on entropy risks amplifying irrelevant tokens and destabilizing training. This paper investigates the exploration dynamics within RLVR and identifies a key issue: the gradual elimination of valuable low-probability exploratory tokens, which we term \textbf{\textit{reasoning sparks}}. We find that while abundant in pre-trained models, these sparks are systematically extinguished during RLVR due to over-penalization, leading to a degeneracy in exploration. To address this, we introduce Low-probability Regularization (Lp-Reg). Its core mechanism regularizes the policy towards a heuristic proxy distribution. This proxy is constructed by filtering out presumed noise tokens and re-normalizing the distribution over the remaining candidates. The result is a less-noisy proxy where the probability of \textit{reasoning sparks} is amplified, which then serves as a soft regularization target to shield these valuable tokens from elimination via KL divergence. Experiments show that Lp-Reg enables stable on-policy training for around 1,000 steps, a regime where baseline entropy-control methods collapse. This sustained exploration leads to state-of-the-art performance, achieving a $60.17\%$ average accuracy on five math benchmarks, an improvement of $2.66\%$ over prior methods. Code is available at https://github.com/CarlanLark/Lp-Reg.

Training Large Language Models (LLMs) for reasoning tasks is increasingly driven by Reinforcement Learning with Verifiable Rewards (RLVR), where Proximal Policy Optimization (PPO) provides a principled framework for stable policy updates. However, the practical application of PPO is hindered by unreliable advantage estimation in the sparse-reward RLVR regime. This issue arises because the sparse rewards in RLVR lead to inaccurate intermediate value predictions, which in turn introduce significant bias when aggregated at every token by Generalized Advantage Estimation (GAE). To address this, we introduce Segmental Advantage Estimation (SAE), which mitigates the bias that GAE can incur in RLVR. Our key insight is that aggregating $n$-step advantages at every token(as in GAE) is unnecessary and often introduces excessive bias, since individual tokens carry minimal information. Instead, SAE first partitions the generated sequence into coherent sub-segments using low-probability tokens as heuristic boundaries. It then selectively computes variance-reduced advantage estimates only from these information-rich segment transitions, effectively filtering out noise from intermediate tokens. Our experiments demonstrate that SAE achieves superior performance, with marked improvements in final scores, training stability, and sample efficiency. These gains are shown to be consistent across multiple model sizes, and a correlation analysis confirms that our proposed advantage estimator achieves a higher correlation with an approximate ground-truth advantage, justifying its superior performance.

LLM agents have emerged as powerful systems for tackling multi-turn tasks by interleaving internal reasoning and external tool interactions. Agentic Reinforcement Learning has recently drawn significant research attention as a critical post-training paradigm to further refine these capabilities. In this paper, we present AT²PO (**A**gentic **T**urn-based **P**olicy **O**ptimization via **T**ree Search), a unified framework for multi-turn agentic RL that addresses three core challenges: limited exploration diversity, sparse credit assignment, and misaligned policy optimization. AT²PO introduces a turn-level tree structure that jointly enables Entropy-Guided Tree Expansion for strategic exploration and Turn-wise Credit Assignment for fine-grained reward propagation from sparse outcomes. Complementing this, we propose Agentic Turn-based Policy Optimization, a turn-level learning objective that aligns policy updates with the natural decision granularity of agentic interactions. ATPO is orthogonal to tree search and can be readily integrated into any multi-turn RL pipeline. Experiments across seven benchmarks demonstrate consistent improvements over the state-of-the-art baseline by up to 1.84 percentage points in average, with ablation studies validating the effectiveness of each component.

Model-based offline reinforcement learning (RL) algorithms have emerged as a promising paradigm for offline RL. These algorithms usually learn a dynamics model from a static dataset of transitions, use the model to generate synthetic trajectories, and perform conservative policy optimization within these trajectories. However, our observations indicate that policy optimization methods used in these model-based offline RL algorithms are not effective at exploring the learned model and induce biased exploration, which ultimately impairs the performance of the algorithm. To address this issue, we propose Offline Conservative ExplorAtioN (OCEAN), a novel rollout approach to model-based offline RL. In our method, we incorporate additional exploration techniques and introduce three conservative constraints based on uncertainty estimation to mitigate the potential impact of significant dynamic errors resulting from exploratory transitions. Our work is a plug-in method and can be combined with classical model-based RL algorithms, such as MOPO, COMBO, and RAMBO. Experiment results of our method on the D4RL MuJoCo benchmark show that OCEAN significantly improves the performance of existing algorithms.

Research on emergent communication has recently gained significant traction as a promising avenue for the linguistic community to unravel human language's origins and explore artificial intelligence's generalization capabilities. Current research has predominantly concentrated on recognizing qualitative patterns of object attributes(e.g., shape and color) and paid little attention to the quantitative relationship among object quantities which is known as the part of numerical concepts. The ability to generalize numerical concepts, i.e., counting and calculations with unseen quantities, is essential, as it mirrors humans' foundational abstract reasoning abilities. In this work, we introduce the NumGame, leveraging the referential game framework, forcing agents to communicate and generalize the numerical concepts effectively. Inspired by the human learning process of numbers, we present a two-stage training approach that sequentially fosters a rudimentary numerical sense followed by the ability of arithmetic calculation, ultimately aiding agents in generating semantically stable and unambiguous language for numerical concepts. The experimental results indicate the impressive generalization capabilities to unseen quantities and regularity of the language emergence from communication.

Large language models (LLMs) show their powerful automatic reasoning and planning capability with a wealth of semantic knowledge about the human world. However, the grounding problem still hinders the applications of LLMs in the real-world environment. Existing studies try to fine-tune the LLM or utilize pre-defined behavior APIs to bridge the LLMs and the environment, which not only costs huge human efforts to customize for every single task but also weakens the generality strengths of LLMs. To autonomously ground the LLM onto the environment, we proposed the Hypothesis, Verification, and Induction (HYVIN) framework to automatically and progressively ground the LLM with self-driven skill learning. HYVIN first employs the LLM to propose the hypothesis of sub-goals to achieve tasks and then verify the feasibility of the hypothesis via interacting with the underlying environment. Once verified, HYVIN can then learn generalized skills with the guidance of these successfully grounded subgoals. These skills can be further utilized to accomplish more complex tasks that fail to pass the verification phase. Verified in the famous instruction following task set, BabyAI, HYVIN achieves comparable performance in the most challenging tasks compared with imitation learning methods that cost millions of demonstrations, proving the effectiveness of learned skills and showing the feasibility and efficiency of our framework.

Overfitting in RL has become one of the main obstacles to applications in reinforcement learning(RL). Existing methods do not provide explicit semantic constrain for the feature extractor, hindering the agent from learning a unified cross-domain representation and resulting in performance degradation on unseen domains. Besides, abundant data from multiple domains are needed. To address these issues, in this work, we propose prompt-based visual alignment (PVA), a robust framework to mitigate the detrimental domain bias in the image for zero-shot policy transfer. Inspired that Visual-Language Model (VLM) can serve as a bridge to connect both text space and image space, we leverage the semantic information contained in a text sequence as an explicit constraint to train a visual aligner. Thus, the visual aligner can map images from multiple domains to a unified domain and achieve good generalization performance. To better depict semantic information, prompt tuning is applied to learn a sequence of learnable tokens. With explicit constraints of semantic information, PVA can learn unified cross-domain representation under limited access to cross-domain data and achieves great zero-shot generalization ability in unseen domains. We verify PVA on a vision-based autonomous driving task with CARLA simulator. Experiments show that the agent generalizes well on unseen domains under limited access to multi-domain data.

Deep reinforcement learning (DRL) has led to a wide range of advances in sequential decision-making tasks. However, the complexity of neural network policies makes it difficult to understand and deploy with limited computational resources. Currently, employing compact symbolic expressions as symbolic policies is a promising strategy to obtain simple and interpretable policies. Previous symbolic policy methods usually involve complex training processes and pre-trained neural network policies, which are inefficient and limit the application of symbolic policies. In this paper, we propose an efficient gradient-based learning method named Efficient Symbolic Policy Learning (ESPL) that learns the symbolic policy from scratch in an end-to-end way. We introduce a symbolic network as the search space and employ a path selector to find the compact symbolic policy. By doing so we represent the policy with a differentiable symbolic expression and train it in an off-policy manner which further improves the efficiency. In addition, in contrast with previous symbolic policies which only work in single-task RL because of complexity, we expand ESPL on meta-RL to generate symbolic policies for unseen tasks. Experimentally, we show that our approach generates symbolic policies with higher performance and greatly improves data efficiency for single-task RL. In meta-RL, we demonstrate that compared with neural network policies the proposed symbolic policy achieves higher performance and efficiency and shows the potential to be interpretable.

Large language models (LLMs) show their powerful automatic reasoning and planning capability with a wealth of semantic knowledge about the human world. However, the grounding problem still hinders the applications of LLMs in the real-world environment. Existing studies try to fine-tune the LLM or utilize pre-defined behavior APIs to bridge the LLMs and the environment, which not only costs huge human efforts to customize for every single task but also weakens the generality strengths of LLMs. To autonomously ground the LLM onto the environment, we proposed the Self-Driven Grounding (SDG) framework to automatically and progressively ground the LLM with self-driven skill learning. SDG first employs the LLM to propose the hypothesis of sub-goals to achieve tasks and then verify the feasibility of the hypothesis via interacting with the underlying environment. Once verified, SDG can then learn generalized skills with the guidance of these successfully grounded subgoals. These skills can be further utilized to accomplish more complex tasks which fail to pass the verification phase. Verified in the famous instruction following task set-BabyAI, SDG achieves comparable performance in the most challenging tasks compared with imitation learning methods that cost millions of demonstrations, proving the effectiveness of learned skills and showing the feasibility and efficiency of our framework.

Domain adaptation in reinforcement learning (RL) mainly deals with the changes of observation when transferring the policy to a new environment. Many traditional approaches of domain adaptation in RL manage to learn a mapping function between the source and target domain in explicit or implicit ways. However, they typically require access to abundant data from the target domain. Besides, they often rely on visual clues to learn the mapping function and may fail when the source domain looks quite different from the target domain. To address these problems, we propose a novel framework Online Prototype Alignment (OPA) to learn the mapping function based on the functional similarity of elements and is able to achieve the few-shot policy transfer within only several episodes. The key insight of OPA is to introduce an exploration mechanism that can interact with the unseen elements of the target domain in an efficient and purposeful manner, and then connect them with the seen elements in the source domain according to their functionalities (instead of visual clues). Experimental results show that when the target domain looks visually different from the source domain, OPA can achieve better transfer performance even with much fewer samples from the target domain, outperforming prior methods.

In the field of multi-task reinforcement learning, the modular principle, which involves specializing functionalities into different modules and combining them appropriately, has been widely adopted as a promising approach to prevent the negative transfer problem that performance degradation due to conflicts between tasks. However, most of the existing multi-task RL methods only combine shared modules at the task level, ignoring that there may be conflicts within the task. In addition, these methods do not take into account that without constraints, some modules may learn similar functions, resulting in restricting the model's expressiveness and generalization capability of modular methods. In this paper, we propose the Contrastive Modules with Temporal Attention(CMTA) method to address these limitations. CMTA constrains the modules to be different from each other by contrastive learning and combining shared modules at a finer granularity than the task level with temporal attention, alleviating the negative transfer within the task and improving the generalization ability and the performance for multi-task RL. We conducted the experiment on Meta-World, a multi-task RL benchmark containing various robotics manipulation tasks. Experimental results show that CMTA outperforms learning each task individually for the first time and achieves substantial performance improvements over the baselines.

Research on emergent communication between deep-learning-based agents has received extensive attention due to its inspiration for linguistics and artificial intelligence. However, previous attempts have hovered around emerging communication under perception-oriented environmental settings, that forces agents to describe low-level perceptual features intra image or symbol contexts. In this work, inspired by the classic human reasoning test (namely Raven's Progressive Matrix), we propose the Reasoning Game, a cognition-oriented environment that encourages agents to reason and communicate high-level rules, rather than perceived low-level contexts. Moreover, we propose 1) an unbiased dataset (namely rule-RAVEN) as a benchmark to avoid overfitting, 2) and a two-stage curriculum agent training method as a baseline for more stable convergence in the Reasoning Game, where contexts and semantics are bilaterally drifting. Experimental results show that, in the Reasoning Game, a semantically stable and compositional language emerges to solve reasoning problems. The emerged language helps agents apply the extracted rules to the generalization of unseen context attributes, and to the transfer between different context attributes or even tasks.

Context-based Meta-Reinforcement Learning (Meta-RL), which conditions the RL agent on the context variables, is a powerful method for learning a generalizable agent. Current context-based Meta-RL methods often construct their contextual policy with a neural network (NN) and directly take the context variables as a part of the input. However, the NN-based policy contains tremendous parameters which possibly result in overfitting, the difficulty of deployment and poor interpretability. To improve the generation ability, efficiency and interpretability, we propose a novel Contextual Symbolic Policy (CSP) framework, which generates contextual policy with a symbolic form based on the context variables for unseen tasks in meta-RL. Our key insight is that the symbolic expression is capable of capturing complex relationships by composing various operators and has a compact form that helps strip out irrelevant information. Thus, the CSP learns to produce symbolic policy for meta-RL tasks and extract the essential common knowledge to achieve higher generalization ability. Besides, the symbolic policies with a compact form are efficient to be deployed and easier to understand. In the implementation, we construct CSP as a gradient-based framework to learn the symbolic policy from scratch in an end-to-end and differentiable way. The symbolic policy is represented by a symbolic network composed of various symbolic operators. We also employ a path selector to decide the proper symbolic form of the policy and a parameter generator to produce the coefficients of the symbolic policy. Empirically, we evaluate the proposed CSP method on several Meta-RL tasks and demonstrate that the contextual symbolic policy achieves higher performance and efficiency and shows the potential to be interpretable.

Despite the broad application of deep reinforcement learning (RL), transferring and adapting the policy to unseen but similar environments is still a significant challenge. Recently, the language-conditioned policy is proposed to facilitate policy transfer through learning the joint representation of observation and text that catches the compact and invariant information across environments. Existing studies of language-conditioned RL methods often learn the joint representation as a simple latent layer for the given instances (episode-specific observation and text), which inevitably includes noisy or irrelevant information and cause spurious correlations that are dependent on instances, thus hurting generalization performance and training efficiency. To address this issue, we propose a conceptual reinforcement learning (CRL) framework to learn the concept-like joint representation for language-conditioned policy. The key insight is that concepts are compact and invariant representations in human cognition through extracting similarities from numerous instances in real-world. In CRL, we propose a multi-level attention encoder and two mutual information constraints for learning compact and invariant concepts. Verified in two challenging environments, RTFM and Messenger, CRL significantly improves the training efficiency (up to 70%) and generalization ability (up to 30%) to the new environment dynamics.

Offline meta-reinforcement learning (OMRL) utilizes pre-collected offline datasets to enhance the agent's generalization ability on unseen tasks. However, the context shift problem arises due to the distribution discrepancy between the contexts used for training (from the behavior policy) and testing (from the exploration policy). The context shift problem leads to incorrect task inference and further deteriorates the generalization ability of the meta-policy. Existing OMRL methods either overlook this problem or attempt to mitigate it with additional information. In this paper, we propose a novel approach called Context Shift Reduction for OMRL (CSRO) to address the context shift problem with only offline datasets. The key insight of CSRO is to minimize the influence of policy in context during both the meta-training and meta-test phases. During meta-training, we design a max-min mutual information representation learning mechanism to diminish the impact of the behavior policy on task representation. In the meta-test phase, we introduce the non-prior context collection strategy to reduce the effect of the exploration policy. Experimental results demonstrate that CSRO significantly reduces the context shift and improves the generalization ability, surpassing previous methods across various challenging domains.

Deep Reinforcement Learning (deep RL) has been successfully applied to solve various decision-making problems in recent years. However, the observations in many real-world tasks are often high dimensional and include much task-irrelevant information, limiting the applications of RL algorithms. To tackle this problem, we propose LCER, a representation learning method that aims to provide RL algorithms with compact and sufficient descriptions of the original observations. Specifically, LCER trains representations to retain the controllable elements of the environment, which can reflect the action-related environment dynamics and thus are likely to be task-relevant. We demonstrate the strength of LCER on the DMControl Suite, proving that it can achieve state-of-the-art performance. LCER enables the pixel-based SAC to outperform state-based SAC on the DMControl 100 K benchmark, showing that the obtained representations can match the oracle descriptions (i.e. the physical states) of the environment. We also carry out experiments to show that LCER can efficiently filter out various distractions, especially when those distractions are not controllable.

Hierarchical reinforcement learning (HRL) effectively improves agents' exploration efficiency on tasks with sparse reward, with the guide of high-quality hierarchical structures (e.g., subgoals or options). However, how to automatically discover high-quality hierarchical structures is still a great challenge. Previous HRL methods can hardly discover the hierarchical structures in complex environments due to the low exploration efficiency by exploiting the randomness-driven exploration paradigm. To address this issue, we propose CDHRL, a causality-driven hierarchical reinforcement learning framework, leveraging a causality-driven discovery instead of a randomness-driven exploration to effectively build high-quality hierarchical structures in complicated environments. The key insight is that the causalities among environment variables are naturally fit for modeling reachable subgoals and their dependencies and can perfectly guide to build high-quality hierarchical structures. The results in two complex environments, 2D-Minecraft and Eden, show that CDHRL significantly boosts exploration efficiency with the causality-driven paradigm.

Object-oriented reinforcement learning (OORL) is a promising way to improve the sample efficiency and generalization ability over standard RL. Recent works that try to solve OORL tasks without additional feature engineering mainly focus on learning the object representations and then solving tasks via reasoning based on these object representations. However, none of these works tries to explicitly model the inherent similarity between different object instances of the same category. Objects of the same category should share similar functionalities; therefore, the category is the most critical property of an object. Following this insight, we propose a novel framework named Object-Category Aware Reinforcement Learning (OCARL), which utilizes the category information of objects to facilitate both perception and reasoning. OCARL consists of three parts: (1) Category-Aware Unsupervised Object Discovery (UOD), which discovers the objects as well as their corresponding categories; (2) Object-Category Aware Perception, which encodes the category information and is also robust to the incompleteness of (1) at the same time; (3) Object-Centric Modular Reasoning, which adopts multiple independent and object-category-specific networks when reasoning based on objects. Our experiments show that OCARL can improve both the sample efficiency and generalization in the OORL domain.

Policy gradient methods are appealing in deep reinforcement learning but suffer from high variance of gradient estimate. To reduce the variance, the state value function is applied commonly. However, the effect of the state value function becomes limited in stochastic dynamic environments, where the unexpected state dynamics and rewards will increase the variance. In this paper, we propose to replace the state value function with a novel hindsight value function, which leverages the information from the future to reduce the variance of the gradient estimate for stochastic dynamic environments. Particularly, to obtain an ideally unbiased gradient estimate, we propose an information-theoretic approach, which optimizes the embeddings of the future to be independent of previous actions. In our experiments, we apply the proposed hindsight value function in stochastic dynamic environments, including discrete-action environments and continuous-action environments. Compared with the standard state value function, the proposed hindsight value function consistently reduces the variance, stabilizes the training, and improves the eventual policy.