论文检索

Reinforcement Learning · Deep RL

Qinsi Wang, Jinghan Ke, Hancheng Ye, Yueqian Lin, Yuzhe Fu, Jianyi Zhang, Kurt Keutzer, Chenfeng Xu, Yiran Chen

Current Reinforcement Fine-tuning (RFT) paradigms for Large Language Models (LLMs) suffer from sample inefficiency due to the redundant exposure of identical queries under uniform data sampling. While previous work has explored curriculum learning via heuristic difficulty metrics, these strategies exhibit limitations by neglecting the intrinsic learning signals generated by the model itself, thus leading to suboptimal training regimes. In this paper, we identify a model-inherent signal termed *angle concentration* that effectively reflects an LLM's capacity to learn from specific data. We theoretically and empirically demonstrate a correlation between the angular distribution of token hidden state vectors and the resulting gradient, revealing a learning preference for data exhibiting higher angle concentration. Inspired by this finding, we propose GAIN-RL, a Gradient-driven Angle-Informed Navigated RL framework. By leveraging the model's intrinsic angle concentration signal, GAIN-RL dynamically selects training data in each epoch, ensuring consistently impactful gradient updates and thus significantly enhancing overall training efficiency. Empirical evaluations show that GAIN-RL (GRPO) achieves over a 2.5$\times$ acceleration in training efficiency across diverse mathematical and coding tasks and varying model scales. Furthermore, GAIN-RL (GRPO)'s efficient sampling yields data-efficient training, achieving better performance with half the original data compared to vanilla GRPO with full training data.

Deep Learning · Everything Else

Huanyu Liu, Jia Li, Hao Zhu, Kechi Zhang, Yihong Dong, Ge Li

How to design reinforcement learning (RL) tasks that effectively unleash the reasoning capability of large language models (LLMs) remains an open question. Existing RL tasks (e.g., math, programming, and constructing reasoning tasks) suffer from three key limitations: (1) Scalability. They rely heavily on human annotation or expensive LLM synthesis to generate sufficient training data. (2) Verifiability. LLMs' outputs are hard to verify automatically and reliably. (3) Controllable Difficulty. Most tasks lack fine-grained difficulty control, making it hard to train LLMs to develop reasoning ability from easy to hard. To address these limitations, we propose Saturn, a SAT-based RL framework that uses Boolean Satisfiability (SAT) problems to train and evaluate LLMs reasoning. Saturn enables scalable task construction, rule-based verification, and precise difficulty control. Saturn designs a curriculum learning pipeline that continuously improves LLMs' reasoning capability by constructing SAT tasks of increasing difficulty and training LLMs from easy to hard. To ensure stable training, we design a principled mechanism to control difficulty transitions. We introduce Saturn-2.6k, a dataset of 2,660 SAT problems with varying difficulty. It supports the evaluation of how LLM reasoning changes with problem difficulty. We apply Saturn to DeepSeek-R1-Distill-Qwen and obtain Saturn-1.5B and Saturn-7B. We achieve several notable results: (1) On SAT problems, Saturn-1.5B and Saturn-7B achieve average pass@3 improvements of +14.0 and +28.1, respectively. (2) On math and programming tasks, Saturn-1.5B and Saturn-7B improve average scores by +4.9 and +1.8 on benchmarks (e.g., AIME, LiveCodeBench). (3) Compared to the state-of-the-art (SOTA) approach in constructing RL tasks, Saturn achieves further improvements of +8.8\%. We release the source code, data, and models to support future research.

Reinforcement Learning · Deep RL

Ahmet Hamdi Güzel, Matthew T Jackson, Jarek Liesen, Tim Rocktäschel, Jakob Foerster, Ilija Bogunovic, Jack Parker-Holder

Training agents to act in embodied environments typically requires vast training data or access to accurate simulation, neither of which exists for many cases in the real world. Instead, world models are emerging as an alternative–leveraging offline, passively collected data, they make it possible to generate diverse worlds for training agents in simulation. In this work, we harness world models to generate “imagined” environments to train robust agents capable of generalizing to novel task variations. One of the challenges in doing this is ensuring the agent trains on useful generated data. We thus propose a novel approach IMAC (Imagined Autocurricula) leveraging Unsupervised Environment Design (UED), induces an automatic curriculum over generated worlds. In a series of challenging, procedurally generated environments, we show it is possible to achieve strong transfer performance on held-out environments having trained only inside a world model learned from a narrower dataset. We believe this opens the path to utilizing larger-scale, foundation world models for generally capable agents.

Reinforcement Learning · Deep RL

Eduardo Pignatelli, Jarek Liesen, Robert Lange, Chris Lu, Pablo Samuel Castro, Laura Toni

As Deep Reinforcement Learning (Deep RL) research moves towards solving large-scale worlds, efficient environment simulations become crucial for rapid experimentation. However, most existing environments struggle to scale to high throughput, setting back meaningful progress. Interactions are typically computed on the CPU, limiting training speed and throughput, due to slower computation and communication overhead when distributing the task across multiple machines. Ultimately, Deep RL training is CPU-bound, and developing batched, fast, and scalable environments has become a frontier for progress. Among the most used Reinforcement Learning (RL) environments, MiniGrid is at the foundation of several studies on exploration, curriculum learning, representation learning, diversity, meta-learning, credit assignment, and language-conditioned RL, and still suffers from the limitations described above. In this work, we introduce NAVIX, a re-implementation of MiniGrid in JAX. NAVIX achieves over $160\,000\times$ speed improvements in batch mode, supporting up to 2048 agents in parallel on a single Nvidia A100 80 GB. This reduces experiment times from one week to 15 minutes, promoting faster design iterations and more scalable RL model development.

Reinforcement Learning · Deep RL

Jin Zhou, Kaiwen Wang, Jonathan Chang, Zhaolin Gao, Nathan Kallus, Kilian Weinberger, Kianté Brantley, Wen Sun

Reinforcement learning (RL) post-training is crucial for LLM alignment and reasoning, but existing policy-based methods, such as PPO and DPO, can fall short of fixing shortcuts inherited from pre-training. In this work, we introduce $Q\sharp$, a value-based algorithm for KL-regularized RL that guides the reference policy using the optimal regularized $Q$ function. We propose to learn the optimal $Q$ function using distributional RL on an aggregated online dataset. Unlike prior value-based baselines that guide the model using unregularized $Q$-values, our method is theoretically principled and provably learns the optimal policy for the KL-regularized RL problem. Empirically, $Q\sharp$ outperforms prior baselines in math reasoning benchmarks while maintaining a smaller KL divergence to the reference policy. Theoretically, we establish a reduction from KL-regularized RL to no-regret online learning, providing the first bounds for deterministic MDPs under only realizability. Thanks to distributional RL, our bounds are also variance-dependent and converge faster when the reference policy has small variance. In sum, our results highlight $Q\sharp$ as an effective approach for post-training LLMs, offering both improved performance and theoretical guarantees. The code can be found at \url{https://github.com/jinpz/q_sharp}.

Reinforcement Learning · Deep RL

Ionel-Alexandru Hosu, Traian Rebedea, Razvan Pascanu

One proposed mechanism to improve exploration in reinforcement learning is the use of macro-actions, a form of temporal abstractions over actions. Paradoxically though, in many scenarios the naive addition of macro-actions does not lead to better exploration, but rather the opposite. In this work, we argue that the difficulty stems from the trade-offs between reducing the average number of decisions per episode versus increasing the size of the action space. Namely, one typically treats each potential macro-action as independent and atomic, hence strictly increasing the search space and making typical exploration strategies inefficient. To address this problem we propose a novel regularization term that exploits the relationship between actions and macro-actions to improve the credit assignment mechanism reducing the effective dimension of the action space and therefore improving exploration. The term relies on a similarity matrix that is meta-learned jointly with learning the desired policy. We empirically validate our strategy looking at macro-actions in Atari games, and the StreetFighter II environment. Our results show significant improvements over the Rainbow-DQN baseline in all environments. Additionally, we show that the macro-action similarity is transferable to other environments with similar dynamics. We believe this work is a small but important step towards understanding how the similarity-imposed geometry on the action space can be exploited to improve credit assignment and exploration, therefore making learning more efficient.

Reinforcement Learning · Deep RL

Haoru Tan, Xiuzhe Wu, Sitong Wu, Shaofeng Zhang, Yanfeng Chen, Xingwu Sun, Jeanne Shen, Xiaojuan Qi

Reinforcement fine-tuning (RFT) is essential for enhancing the reasoning and generalization capabilities of large language models, but its success heavily relies on the quality of the training data. While data selection has been extensively studied in supervised learning, its role in reinforcement learning, particularly during the RFT stage, remains largely underexplored. In this work, we introduce RFT-Inf, the first influence estimator designed for data in reinforcement learning. RFT-Inf quantifies the importance of each training example by measuring how its removal affects the final training reward, offering a direct estimate of its contribution to model learning. To ensure scalability, we propose a first-order approximation of the RFT-Inf score by backtracking through the optimization process and applying temporal differentiation to the sample-wise influence term, along with a first-order Taylor approximation to adjacent time steps. This yields a lightweight, gradient-based estimator that evaluates the alignment between an individual sample’s gradient and the average gradient direction of all training samples, where a higher degree of alignment implies greater training utility. Extensive experiments demonstrate that RFT-Inf consistently improves reward performance and accelerates convergence in reinforcement fine-tuning.

Deep Learning · Generative Models and Autoencoders

Gang Li, Ming Lin, Tomer Galanti, Zhengzhong Tu, Tianbao Yang

The recent success and openness of DeepSeek-R1 have brought widespread attention to Group Relative Policy Optimization (GRPO) as a reinforcement learning method for large reasoning models (LRMs). In this work, we analyze the GRPO objective under a binary reward setting and reveal an inherent limitation of question-level difficulty bias arising from its group relative advantage function. We also identify a connection between GRPO and traditional discriminative methods in supervised learning. Motivated by these insights, we introduce a new **Discriminative Constrained Optimization (DisCO)** framework for reinforcing LRMs, grounded in the principle of discriminative learning: increasing the scores of positive answers while decreasing those of negative ones. The main differences between DisCO and GRPO and its recent variants are: (1) it replaces the group relative objective with a discriminative objective defined by a scoring function; (2) it abandons clipping-based surrogates in favor of non-clipping RL surrogate objectives used as scoring functions; (3) it employs a simple yet effective constrained optimization approach to enforce the KL divergence constraint. As a result, DisCO offers notable advantages over GRPO and its variants: (i) it completely eliminates difficulty bias by adopting discriminative objectives; (ii) it addresses the entropy instability in GRPO and its variants through the use of non-clipping scoring functions and a constrained optimization approach, yielding long and stable training dynamics; (iii) it allows the incorporation of advanced discriminative learning techniques to address data imbalance, where a significant number of questions have more negative than positive generated answers during training. Our experiments on enhancing the mathematical reasoning capabilities of SFT-finetuned models show that DisCO significantly outperforms GRPO and its improved variants such as DAPO, achieving average gains of 7\% over GRPO and 6\% over DAPO across six benchmark tasks for an 1.5B model.

Reinforcement Learning · Deep RL

Yizhen Zhang, Yang Ding, Shuoshuo Zhang, Xinchen Zhang, Haoling Li, Zhong-Zhi Li, Peijie Wang, Jie Wu, Lei Ji, Yeyun Gong 等

Inspired by the impressive reasoning capabilities demonstrated by reinforcement learning approaches like DeepSeek-R1, recent emerging research has begun exploring the use of reinforcement learning (RL) to enhance vision-language models (VLMs) for multimodal reasoning tasks. However, most existing multimodal reinforcement learning approaches remain limited to spatial reasoning within single-image contexts, yet still struggle to generalize to more complex and real-world scenarios involving multi-image positional reasoning, where understanding the relationships across images is crucial. To address this challenge, we propose a general reinforcement learning approach PeRL tailored for interleaved multimodal tasks, and a multi-stage strategy designed to enhance the exploration-exploitation trade-off, thereby improving learning efficiency and task performance. Specifically, we introduce permutation of image sequences to simulate varied positional relationships to explore more spatial and positional diversity. Furthermore, we design a rollout filtering mechanism for resampling to focus on trajectories that contribute most to learning optimal behaviors to exploit learned policies effectively. We evaluate our model on 5 widely-used multi-image benchmarks and 3 single-image benchmarks. Our experiments confirm that PeRL trained model consistently surpasses R1-related and interleaved VLM baselines by a large margin, achieving state-of-the-art performance on multi-image benchmarks, while preserving comparable performance on single-image tasks.

Reinforcement Learning · Deep RL

Michal Nauman, Marek Cygan, Carmelo Sferrazza, Aviral Kumar, Pieter Abbeel

Recent advances in language modeling and vision stem from training large models on diverse, multi‑task data. This paradigm has had limited impact in value-based reinforcement learning (RL), where improvements are often driven by small models trained in a single-task context. This is because in multi-task RL sparse rewards and gradient conflicts make optimization of temporal difference brittle. Practical workflows for generalist policies therefore avoid online training, instead cloning expert trajectories or distilling collections of single‑task policies into one agent. In this work, we show that the use of high-capacity value models trained via cross-entropy and conditioned on learnable task embeddings addresses the problem of task interference in online RL, allowing for robust and scalable multi‑task training. We test our approach on 7 multi-task benchmarks with over 280 unique tasks, spanning high degree-of-freedom humanoid control and discrete vision-based RL. We find that, despite its simplicity, the proposed approach leads to state-of-the-art single and multi-task performance, as well as sample-efficient transfer to new tasks.

Reinforcement Learning · Deep RL

Guojian Zhan, Likun Wang, Xiangteng Zhang, Jiaxin Gao, Masayoshi TOMIZUKA, Shengbo Li

Online planning has proven effective in reinforcement learning (RL) for improving sample efficiency and final performance. However, using planning for environment interaction inevitably introduces a divergence between the collected data and the policy's actual behaviors, degrading both model learning and policy improvement. To address this, we propose BOOM (Bootstrap Off-policy with WOrld Model), a framework that tightly integrates planning and off-policy learning through a bootstrap loop: the policy initializes the planner, and the planner refines actions to bootstrap the policy through behavior alignment. This loop is supported by a jointly learned world model, which enables the planner to simulate future trajectories and provides value targets to facilitate policy improvement. The core of BOOM is a likelihood-free alignment loss that bootstraps the policy using the planner’s non-parametric action distribution, combined with a soft value-weighted mechanism that prioritizes high-return behaviors and mitigates variability in the planner’s action quality within the replay buffer. Experiments on the high-dimensional DeepMind Control Suite and Humanoid-Bench show that BOOM achieves state-of-the-art results in both training stability and final performance. The code is accessible at \url{https://github.com/molumitu/BOOM_MBRL}.

Deep Learning · Generative Models and Autoencoders

Keuntae Kim, Eunhye Jeong, Sehyeon Lee, Seohee Yoon, Yong Suk Choi

Recent advances in enhancing the reasoning ability of Large Language Models (LLMs) have been remarkably successful. LLMs trained with Reinforcement Learning (RL) for reasoning demonstrate strong performance in challenging tasks such as mathematics and coding, even with relatively small model sizes. However, despite these impressive improvements in task accuracy, the assessment of creativity in LLM generations has been largely overlooked in reasoning tasks, in contrast to writing tasks. The lack of research on creativity assessment in reasoning primarily stems from two challenges: (1) the difficulty of defining the range of creativity, and (2) the necessity of human evaluation in the assessment process. To address these challenges, we propose CLAWS, a novel method that defines and classifies mathematical solutions into Typical, Creative, and Hallucinated categories without human evaluation, by leveraging attention weights across prompt sections and output. CLAWS outperforms five existing white-box detection methods—Perplexity, Logit Entropy, Window Entropy, Hidden Score, and Attention Score—on five 7–8B math RL models (DeepSeek, Qwen, Mathstral, OpenMath2, and Oreal). We validate CLAWS on 4,545 math problems collected from 181 math contests (A(J)HSME, AMC, AIME). Our code is available at https://github.com/kkt94/CLAWS.

Deep Learning · Everything Else

Chenrui Cao, Liangcheng Song, Zenan Li, Xinyi Le, Xian Zhang, HUI XUE, Fan Yang

Recent advancements, such as DeepSeek-Prover-V2-671B and Kimina-Prover-Preview-72B, demonstrate a prevailing trend in leveraging reinforcement learning (RL)-based large-scale training for automated theorem proving. Surprisingly, we discover that even without any training, careful neuro-symbolic coordination of existing off-the-shelf reasoning models and tactic step provers can achieve comparable performance. This paper introduces DSP+, an improved version of the Draft, Sketch, and Prove framework, featuring a fine-grained and integrated neuro-symbolic enhancement for each phase: (1) In the draft phase, we prompt reasoning models to generate concise natural-language subgoals to benefit the sketch phase, removing thinking tokens and references to human-written proofs; (2) In the sketch phase, subgoals are autoformalized with hypotheses to benefit the proving phase, and sketch lines containing syntactic errors are masked according to predefined rules; (3) In the proving phase, we tightly integrate symbolic search methods like Aesop with step provers to establish proofs for the sketch subgoals. Experimental results show that, without any additional model training or fine-tuning, DSP+ solves 80.7%, 32.8%, and 24 out of 644 problems from miniF2F, ProofNet, and PutnamBench, respectively, while requiring fewer budgets compared to state-of-the-arts. DSP+ proves imo_2019_p1, an IMO problem in miniF2F that is not solved by any prior work. Additionally, DSP+ generates proof patterns comprehensible by human experts, facilitating the identification of formalization errors; For example, eight wrongly formalized statements in miniF2F are discovered. Our results highlight the potential of classical reasoning patterns besides the RL-based training. All components will be open-sourced.

Reinforcement Learning · Deep RL

Finn Rietz, Oleg Smirnov, Sara Karimi, Lele Cao

Prompt tuning has emerged as a key technique for adapting large pre-trained Decision Transformers (DTs) in offline Reinforcement Learning (RL), particularly in multi-task and few-shot settings. The Prompting Decision Transformer (PDT) enables task generalization via trajectory prompts sampled uniformly from expert demonstrations -- without accounting for prompt informativeness. In this work, we propose a bandit-based prompt-tuning method that learns to construct optimal trajectory prompts from demonstration data at inference time. We devise a structured bandit architecture operating in the trajectory prompt space, achieving linear rather than combinatorial scaling with prompt size. Additionally, we show that the pre-trained PDT itself can serve as a powerful feature extractor for the bandit, enabling efficient reward modeling across various environments. We theoretically establish regret bounds and demonstrate empirically that our method consistently enhances performance across a wide range of tasks, high-dimensional environments, and out-of-distribution scenarios, outperforming existing baselines in prompt tuning.

Reinforcement Learning · Deep RL

Haizhong Zheng, Yang Zhou, Brian Bartoldson, Bhavya Kailkhura, Fan Lai, Jiawei Zhao, Beidi Chen

Reinforcement learning, such as PPO and GRPO, has powered recent breakthroughs in LLM reasoning. Scaling rollout to sample more prompts enables models to selectively use higher-quality data for training, which can stabilize RL training and improve model performance, but at the cost of significant computational overhead. In this paper, we first show that a substantial portion of this overhead can be avoided by skipping uninformative prompts before rollout. Our analysis of reward dynamics reveals a strong temporal consistency in prompt value: prompts that are uninformative in one epoch of training are likely to remain uninformative in near future epochs. Based on these insights, we propose GRESO (GRPO with Efficient Selective Rollout), an online, lightweight pre-rollout filtering algorithm that predicts and skips uninformative prompts using reward training dynamics. By evaluating GRESO on a broad range of math reasoning benchmarks and models, like Qwen2.5-Math-1.5B, DeepSeek-R1-Distill-Qwen-1.5B, Qwen2.5-Math-7B, Qwen2.5-14B, and Qwen2.5-32B, we show that GRESO achieves up to 2.4x wall-clock time speedup in rollout and up to 2.0x speedup in total training time without accuracy degradation. We make our code publicly available at https://github.com/Infini-AI-Lab/GRESO/.

Reinforcement Learning · Deep RL

Jijia Liu, Feng Gao, Bingwen Wei, Xinlei Chen, Qingmin Liao, YI WU, Chao Yu, Yu Wang

Large Vision-Language Action (VLA) models have shown significant potential for embodied AI. However, their predominant training via supervised fine-tuning (SFT) limits generalization due to susceptibility to compounding errors under distribution shifts. Reinforcement learning (RL) offers a path to overcome these limitations by optimizing for task objectives via trial-and-error, yet a systematic understanding of its specific generalization benefits for VLAs compared to SFT is lacking. To address this, our study introduces a comprehensive benchmark for evaluating VLA generalization and systematically investigates the impact of RL fine-tuning across diverse visual, semantic, and execution dimensions. Our extensive experiments reveal that RL fine-tuning, particularly with PPO, significantly enhances generalization in semantic understanding and execution robustness over SFT, while maintaining comparable visual robustness. We identify PPO as a more effective RL algorithm for VLAs than LLM-derived methods like DPO and GRPO. We also develop a simple recipe for efficient PPO training on VLAs, and demonstrate its practical utility for improving VLA generalization. The project page is at https://rlvla.github.io

General Machine Learning · Everything Else

Marzi Heidari, Hanping Zhang, Yuhong Guo

The challenge of learning with noisy labels is significant in machine learning, as it can severely degrade the performance of prediction models if not addressed properly. This paper introduces a novel framework that conceptualizes noisy label correction as a reinforcement learning (RL) problem. The proposed approach, Reinforcement Learning for Noisy Label Correction (RLNLC), defines a comprehensive state space representing data and their associated labels, an action space that indicates possible label corrections, and a reward mechanism that evaluates the efficacy of label corrections. RLNLC learns a deep feature representation based policy network to perform label correction through reinforcement learning, utilizing an actor-critic method. The learned policy is subsequently deployed to iteratively correct noisy training labels and facilitate the training of the prediction model. The effectiveness of RLNLC is demonstrated through extensive experiments on multiple benchmark datasets, where it consistently outperforms existing state-of-the-art techniques for learning with noisy labels.

Reinforcement Learning · Deep RL

Nicolas Castanet, Olivier Sigaud, Sylvain Lamprier

Goal-Conditioned Reinforcement Learning (GCRL) enables agents to autonomously acquire diverse behaviors, but faces major challenges in visual environments due to high-dimensional, semantically sparse observations. In the online setting, where agents learn representations while exploring, the latent space evolves with the agent's policy, to capture newly discovered areas of the environment. However, without incentivization to maximize state coverage in the representation, classical approaches based on auto-encoders may converge to latent spaces that over-represent a restricted set of states frequently visited by the agent. This is exacerbated in an intrinsic motivation setting, where the agent uses the distribution encoded in the latent space to sample the goals it learns to master. To address this issue, we propose to progressively enforce distributional shifts towards a uniform distribution over the full state space, to ensure a full coverage of skills that can be learned in the environment. We introduce DRAG (Distributionally Robust Auto-Encoding for GCRL), a method that combines the $\beta$-VAE framework with Distributionally Robust Optimization (DRO). DRAG leverage an adversarial neural weighter of training states of the VAE, to account for the mismatch between the current data distribution and unseen parts of the environment. This allows the agent to construct semantically meaningful latent spaces beyond its immediate experience. Our approach improves state space coverage and downstream control performance on hard exploration environments such as mazes and robotic control involving walls to bypass, without relying on pre-training nor prior environment knowledge.

Reinforcement Learning · Deep RL

Yihuan Mao, Chongjie Zhang

Given the ever-changing nature of the world and its inhabitants, agents must possess the ability to adapt and evolve over time. Recent research in Given the ever-changing nature of the world and its inhabitants, agents must possess the ability to adapt and evolve over time. Recent research in non-stationary MDPs has focused on addressing this challenge, providing algorithms inspired by task inference techniques. However, these methods ignore the detrimental effects of interference, which particularly harm performance in contradictory tasks, leading to low efficiency in some environments. To address this issue, we propose a Bayesian Fast-Slow Framework (BFSF) that tackles both cross-task generalization and resistance to cross-task interference. Our framework consists of two components: a 'fast' policy, learned from recent data, and a 'slow' policy, learned through meta-reinforcement learning (meta-RL) using data from all previous tasks. A Bayesian estimation mechanism determines the current choice of 'fast' or 'slow' policy, balancing exploration and exploitation. Additionally, in the 'fast' policy, we introduce a dual-reset mechanism and a data relabeling technique to further accelerate convergence when encountering new tasks. Experiments demonstrate that our algorithm effectively mitigates interference and outperforms baseline approaches.

Deep Learning · Algorithms

Kongcheng Zhang, QI YAO, Shunyu Liu, Yingjie Wang, Baisheng Lai, Jieping Ye, Mingli Song, Dacheng Tao

Recent advances of Reinforcement Learning (RL) have highlighted its potential in complex reasoning tasks, yet effective training often relies on external supervision, which limits the broader applicability. In this work, we propose a novel self-rewarding reinforcement learning framework to enhance Large Language Model (LLM) reasoning by leveraging the consistency of intermediate reasoning states across different reasoning trajectories. Our key insight is that correct responses often exhibit consistent trajectory patterns in terms of model likelihood: their intermediate reasoning states tend to converge toward their own final answers (*high consistency*) with minimal deviation toward other candidates (*low volatility*). Inspired by this observation, we introduce CoVo, an intrinsic reward mechanism that integrates ***Co***nsistency and ***Vo***latility via a robust vector-space aggregation strategy, complemented by a curiosity bonus to promote diverse exploration. CoVo enables LLMs to perform RL in a self-rewarding manner, offering a scalable pathway for learning to reason without external supervision. Extensive experiments on diverse reasoning benchmarks show that CoVo achieves performance comparable to or even surpassing supervised RL. Our code is available at https://github.com/sastpg/CoVo.