Reasoning with Exploration: An Entropy Perspective
Daixuan Cheng, Shaohan Huang, Xuekai Zhu, Bo Dai, Xin Zhao, Zhenliang Zhang, Furu Wei
Abstract
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 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 deeper and longer 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.
Ask about this paper
Your agent reads all of it.
Lune indexed this paper to the last equation, along with the top-tier papers that cite it. Ask a question and the answer quotes them.
Your agent calls
Luneget_paper_fulltext
Free to start. No credit card required.
Terminal
Install the CLIlune papers fulltext 4f2e6738-85ab-4b87-9ff6-63ef36ae0475Cited by top-tier papers89
- R-Zero: Self-Evolving Reasoning LLM from Zero DataChengsong Huang, Wenhao Yu, Xiaoyang Wang, Hongming Zhang et al.ICLR 2026 · 220 citations
- Agentic Reinforced Policy OptimizationGuanting Dong, Hangyu Mao, Kai Ma, Licheng Bao et al.ICLR 2026 · 146 citations
- Geometric-Mean Policy OptimizationYuzhong Zhao, Yue Liu, Junpeng Liu, Jingye Chen et al.ICLR 2026 · 104 citations
- Learning What Reinforcement Learning Can't: Interleaved Online Fine-Tuning for Hardest QuestionsLu Ma, Hao Liang, Meiyi Qiang, Lexiang Tang et al.ICLR 2026 · 103 citations
- Entropy-Aware On-Policy Distillation of Language ModelsWoogyeol Jin, Taywon Min, Yongjin Yang, Dennis Wei et al.ICML 2026 · 91 citations
Builds on16
- Training language models to follow instructions with human feedbackLong Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida et al.NeurIPS 2022 · 24,707 citations
- DAPO: An Open-Source LLM Reinforcement Learning System at ScaleQiying Yu, Zheng Zhang, Ruofei Zhu, Yufeng Yuan et al.NeurIPS 2025 · 2,828 citations
- Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM ReasoningShenzhi Wang, Le Yu, Chang Gao, Chujie Zheng et al.NeurIPS 2025 · 592 citations
- Reinforcement Learning for Reasoning in Large Language Models with One Training ExampleYiping Wang, Qing Yang, Zhiyuan Zeng, Liliang Ren et al.NeurIPS 2025 · 314 citations
- Provably Efficient Exploration in Policy OptimizationQi Cai, Zhuoran Yang, Chi Jin, Zhaoran WangICML 2020 · 304 citations
Related papers
- Rethinking Entropy Interventions in RLVR: An Entropy Change PerspectiveZhezheng Hao, Hong Wang, Haoyang Liu, Jian Luo et al.ACL 2026 · 42 citations
- GTPO and GRPO-S: Token and Sequence-Level Reward Shaping with Policy EntropyHongze Tan, Zihan Wang, Jianfei Pan, Jinghao Lin et al.ICML 2026 · 53 citations
- Heterogeneous Adaptive Policy Optimization: Tailoring Optimization to Every Token's NatureZheng Liu, Mengjie Liu, Siwei Wen, Mengzhang Cai et al.ACL 2026 · 9 citations
- CE-GPPO: Coordinating Entropy via Gradient-Preserving Clipping Policy Optimization in Reinforcement LearningZhenpeng Su, Leiyu Pan, Minxuan Lv, Yuntao Li et al.ACL 2026 · 21 citations
- Emergent Hierarchical Reasoning in LLMs through Reinforcement LearningHaozhe Wang, Qixin Xu, Che Liu, Junhong Wu et al.ICLR 2026 · 44 citations
