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This paper aims to overcome a major obstacle in scaling RL for reasoning with LLMs, namely the collapse of policy entropy. Such phenomenon is consistently observed across vast RL runs without entropy intervention, where the policy entropy…

Long-term training of large language models (LLMs) requires maintaining stable exploration to prevent the model from collapsing into sub-optimal behaviors. Entropy is crucial in this context, as it controls exploration and helps avoid…

Machine Learning · Computer Science 2026-02-03 Kai Yang , Xin Xu , Yangkun Chen , Weijie Liu , Jiafei Lyu , Zichuan Lin , Deheng Ye , Saiyong Yang

Despite the many recent advances in reinforcement learning (RL), the question of learning policies that robustly satisfy state constraints under unknown disturbances remains open. In this paper, we offer a new perspective on achieving…

Machine Learning · Computer Science 2025-12-23 Pierre-François Massiani , Alexander von Rohr , Lukas Haverbeck , Sebastian Trimpe

State entropy regularization has empirically shown better exploration and sample complexity in reinforcement learning (RL). However, its theoretical guarantees have not been studied. In this paper, we show that state entropy regularization…

Machine Learning · Computer Science 2025-12-02 Yonatan Ashlag , Uri Koren , Mirco Mutti , Esther Derman , Pierre-Luc Bacon , Shie Mannor

Reasoning ability has become a defining capability of Large Language Models (LLMs), with Reinforcement Learning with Verifiable Rewards (RLVR) emerging as a key paradigm to enhance it. However, RLVR training often suffers from policy…

Machine Learning · Computer Science 2026-04-20 Xiaoyun Zhang , Xiaojian Yuan , Di Huang , Wang You , Chen Hu , Jingqing Ruan , Ai Jian , Kejiang Chen , Xing Hu

For RL algorithms, appropriate entropy control is crucial to their effectiveness. To control the policy entropy, a commonly used method is entropy regularization, which is adopted in various popular RL algorithms including PPO, SAC and A3C.…

Machine Learning · Computer Science 2026-02-06 Han Shen

Reinforcement learning with verifiable rewards (RLVR) has demonstrated superior performance in enhancing the reasoning capability of large language models (LLMs). However, this accuracy-oriented learning paradigm often suffers from entropy…

Artificial Intelligence · Computer Science 2026-01-19 Hongye Cao , Zhixin Bai , Ziyue Peng , Boyan Wang , Tianpei Yang , Jing Huo , Yuyao Zhang , Yang Gao

Reinforcement Learning with Verifiable Rewards (RLVR) serves as a cornerstone technique for enhancing the reasoning capabilities of Large Language Models (LLMs). However, its training is often plagued by \emph{entropy collapse}, a rapid…

Machine Learning · Computer Science 2026-04-30 Zhezheng Hao , Hong Wang , Haoyang Liu , Jian Luo , Jiarui Yu , Hande Dong , Qiang Lin , Can Wang , Jiawei Chen

Deep Reinforcement Learning (Deep RL) has had incredible achievements on high dimensional problems, yet its learning process remains unstable even on the simplest tasks. Deep RL uses neural networks as function approximators. These neural…

Machine Learning · Computer Science 2022-10-18 Riccardo Della Vecchia , Alena Shilova , Philippe Preux , Riad Akrour

Reinforcement learning with verifiable rewards (RLVR) has emerged as a prominent paradigm for enhancing the reasoning capabilities of large language models (LLMs). However, the entropy of LLMs usually collapses during RLVR training, leading…

Computation and Language · Computer Science 2026-04-21 Renren Jin , Pengzhi Gao , Yuqi Ren , Zhuowen Han , Tongxuan Zhang , Wuwei Huang , Wei Liu , Jian Luan , Deyi Xiong

Reinforcement learning (RL) is a key paradigm for post-training large language models (LLMs), but the widely used Group Relative Policy Optimization (GRPO) often suffers from entropy collapse: exploration quickly disappears, policies…

Machine Learning · Computer Science 2026-05-19 Chen Wang , Zhaochun Li , Jionghao Bai , Hexuan Deng , Ge Lan , Yue Wang

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a critical method for enhancing the reasoning capabilities of Large Language Models (LLMs). However, continuous training often leads to policy entropy collapse,…

Machine Learning · Computer Science 2026-05-11 Kun Chen , Peng Shi , Fanfan Liu , Haibo Qiu , Zhixiong Zeng , Siqi Yang , Wenji Mao

We investigate an entropy-regularized reinforcement learning (RL) approach to optimal stopping problems motivated by real option models. Classical stopping rules are strict and non-randomized, limiting natural exploration in RL settings. To…

Optimization and Control · Mathematics 2026-02-18 Jodi Dianetti , Giorgio Ferrari , Renyuan Xu

Large language models (LLMs) have shown promise in performing complex multi-step reasoning, yet they continue to struggle with mathematical reasoning, often making systematic errors. A promising solution is reinforcement learning (RL)…

Machine Learning · Computer Science 2025-09-22 Hanning Zhang , Pengcheng Wang , Shizhe Diao , Yong Lin , Rui Pan , Hanze Dong , Dylan Zhang , Pavlo Molchanov , Tong Zhang

Dealing with high variance is a significant challenge in model-free reinforcement learning (RL). Existing methods are unreliable, exhibiting high variance in performance from run to run using different initializations/seeds. Focusing on…

Machine Learning · Computer Science 2019-05-15 Richard Cheng , Abhinav Verma , Gabor Orosz , Swarat Chaudhuri , Yisong Yue , Joel W. Burdick

Entropy augmented to reward is known to soften the greedy argmax policy to softmax policy. Entropy augmentation is reformulated and leads to a motivation to introduce an additional entropy term to the objective function in the form of…

Machine Learning · Computer Science 2020-06-08 Donghoon Lee

Reinforcement learning (RL) has enabled complex reasoning abilities in large language models (LLMs). However, most RL algorithms suffer from performance saturation, preventing continued gains as RL training scales. This problem can be…

Machine Learning · Computer Science 2026-05-12 Bolian Li , Yifan Wang , Yi Ding , Anamika Lochab , Ananth Grama , Ruqi Zhang

Reinforcement learning (RL) is an important field of research in machine learning that is increasingly being applied to complex optimization problems in physics. In parallel, concepts from physics have contributed to important advances in…

Machine Learning · Computer Science 2023-05-11 Argenis Arriojas , Jacob Adamczyk , Stas Tiomkin , Rahul V. Kulkarni

This paper explores the impact of dynamic entropy tuning in Reinforcement Learning (RL) algorithms that train a stochastic policy. Its performance is compared against algorithms that train a deterministic one. Stochastic policies optimize a…

Robotics · Computer Science 2025-12-23 Youssef Mahran , Zeyad Gamal , Ayman El-Badawy

Deep Reinforcement Learning (Deep RL) has been receiving increasingly more attention thanks to its encouraging performance on a variety of control tasks. Yet, conventional regularization techniques in training neural networks (e.g., $L_2$…

Machine Learning · Computer Science 2021-11-30 Zhuang Liu , Xuanlin Li , Bingyi Kang , Trevor Darrell
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