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Group Relative Policy Optimization (GRPO) has significantly enhanced the reasoning capability of large language models by optimizing the arithmetic mean of token-level rewards.
Policy gradient methods for reinforcement learning with function approximation
Richard S Sutton, David McAllester, Satinder Singh, and Yishay Mansour · 1999
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Proximal policy optimization algorithms
John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov · 2017
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Measuring mathematical problem solving with the math dataset
Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt · 2021
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Inter-gps: Interpretable geometry problem solving with formal language and symbolic reasoning
Pan Lu, Ran Gong, Shibiao Jiang, Liang Qiu, Siyuan Huang, Xiaodan Liang, and Song-Chun Zhu · 2021
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Solving quantitative reasoning problems with language models
Aitor Lewkowycz, Anders Andreassen, David Dohan, Ethan Dyer, Henryk Michalewski, Vinay Ramasesh, Ambrose Slone, Cem Anil, Imanol Schlag, Theo Gutman-Solo, et al · 2022
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OlympiadBench: A challenging benchmark for promoting AGI with olympiad-level bilingual multimodal scientific problems
Chaoqun He, Renjie Luo, Yuzhuo Bai, Shengding Hu, Zhen Thai, Junhao Shen, Jinyi Hu, Xu Han, Yujie Huang, Yuxiang Zhang, Jie Liu, Lei Qi, Zhiyuan Liu, and Maosong Sun · 2024
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Numinamath: The largest public dataset in ai4maths with 860k pairs of competition math problems and solutions
Jia Li, Edward Beeching, Lewis Tunstall, Ben Lipkin, Roman Soletskyi, Shengyi Huang, Kashif Rasul, Longhui Yu, Albert Q Jiang, Ziju Shen, et al · 2024
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Deepseekmath: Pushing the limits of mathematical reasoning in open language models
Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Y Wu, et al · 2024
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Qwen2. 5-math technical report: Toward mathematical expert model via self-improvement
An Yang, Beichen Zhang, Binyuan Hui, Bofei Gao, Bowen Yu, Chengpeng Li, Dayiheng Liu, Jianhong Tu, Jingren Zhou, Junyang Lin, et al · 2024
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Advancing llm reasoning generalists with preference trees
Lifan Yuan, Ganqu Cui, Hanbin Wang, Ning Ding, Xingyao Wang, Jia Deng, Boji Shan, Huimin Chen, Ruobing Xie, Yankai Lin, et al · 2024
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Shuai Bai, Keqin Chen, Xuejing Liu, Jialin Wang, Wenbin Ge, Sibo Song, Kai Dang, Peng Wang, Shijie Wang, Jun Tang, et al · 2025
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Seed-grpo: Semantic entropy enhanced grpo for uncertainty-aware policy optimization
Minghan Chen, Guikun Chen, Wenguan Wang, and Yi Yang · 2025
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Reasoning with exploration: An entropy perspective
Daixuan Cheng, Shaohan Huang, Xuekai Zhu, Bo Dai, Wayne Xin Zhao, Zhenliang Zhang, and Furu Wei · 2025
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Gpg: A simple and strong reinforcement learning baseline for model reasoning
Xiangxiang Chu, Hailang Huang, Xiao Zhang, Fei Wei, and Yong Wang · 2025
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On-policy rl with optimal reward baseline
Yaru Hao, Li Dong, Xun Wu, Shaohan Huang, Zewen Chi, and Furu Wei · 2025
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Open-reasoner-zero: An open source approach to scaling up reinforcement learning on the base model
Shenzhi Wang, Le Yu, Chang Gao, Chujie Zheng, Shixuan Liu, Rui Lu, Kai Dang, Xionghui Chen, Jianxin Yang, Zhenru Zhang, et al · 2025
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Bnpo: Beta normalization policy optimization
Changyi Xiao, Mengdi Zhang, and Yixin Cao · 2025
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Not all rollouts are useful: Down-sampling rollouts in llm reinforcement learning
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Jingcheng Hu, Yinmin Zhang, Qi Han, Daxin Jiang, Xiangyu Zhang, and Heung-Yeung Shum · 2025
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Repo: Replay-enhanced policy optimization
Siheng Li, Zhanhui Zhou, Wai Lam, Chao Yang, and Chaochao Lu · 2025
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Cppo: Accelerating the training of group relative policy optimization-based reasoning models
Zhihang Lin, Mingbao Lin, Yuan Xie, and Rongrong Ji · 2025
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Understanding r1-zero-like training: A critical perspective
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Qwen2.5 technical report, 2025
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Process reinforcement through implicit rewards
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Dapo: An open-source llm reinforcement learning system at scale
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Learning to reason without external rewards
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