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Group Relative Policy Optimization (GRPO) was introduced and used recently for promoting reasoning in LLMs under verifiable (binary) rewards.
Reinforcement Learning: An Introduction
R. S. Sutton and A. G. Barto · 1998
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Mirror descent policy optimization, 2021
M. Tomar, L. Shani, Y. Efroni, and M. Ghavamzadeh · 2005
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Trust region policy optimization
J. Schulman, S. Levine, P. Abbeel, M. Jordan, and P. Moritz · 2015
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Proximal policy optimization algorithms
J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov · 2017
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PyTorch: An Imperative Style, High-Performance Deep Learning Library, Dec. 2019
A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Köpf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, and S. Chintala · 2019
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Implementation matters in deep rl: A case study on ppo and trpo
L. Engstrom, A. Ilyas, S. Santurkar, D. Tsipras, F. Janoos, L. Rudolph, and A. Madry · 2020
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HuggingFace’s Transformers: State-of-the-art Natural Language Processing, July 2020
T. Wolf, L. Debut, V. Sanh, J. Chaumond, C. Delangue, A. Moi, P. Cistac, T. Rault, R. Louf, M. Funtowicz, J. Davison, S. Shleifer, P. von Platen, C. Ma, Y. Jernite, J. Plu, C. Xu, T. L. Scao, S. Gugger, M. Drame, Q. Lhoest, and A. M. Rush · 2020
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Training verifiers to solve math word problems
K. Cobbe, V. Kosaraju, M. Bavarian, M. Chen, H. Jun, L. Kaiser, M. Plappert, J. Tworek, J. Hilton, R. Nakano, C. Hesse, and J. Schulman · 2021
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Efficient memory management for large language model serving with pagedattention
W. Kwon, Z. Li, S. Zhuang, Y. Sheng, L. Zheng, C. H. Yu, J. E. Gonzalez, H. Zhang, and I. Stoica · 2023
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Apple intelligence foundation language models, 2024
T. Gunter, Z. Wang, C. Wang, R. Pang, A. Narayanan, A. Zhang, B. Zhang, C. Chen, C.-C. Chiu, D. Qiu, D. Gopinath, D. A. Yap, D. Yin, F. Nan, F. Weers, G. Yin, H. Huang, J. Wang, J. Lu, J. Peebles, K. Ye, M. Lee, N. Du, Q. Chen, Q. Keunebroek, S. Wiseman, S. Evans, T. Lei, V. Rathod, X. Kong, X. Du, Y. Li, Y. Wang, Y. Gao, Z. Ahmed, Z. Xu, Z. Lu, A. Rashid, A. M. Jose, A. Doane, A. Bencomo, A. Vanderby, A. Hansen, A. Jain, A. M. Anupama, A. Kamal, B. Wu, C. Brum, C. Maalouf, C. Erdenebileg, C. Dulhanty, D. Moritz, D. Kang, E. Jimenez, E. Ladd, F. Shi, F. Bai, F. Chu, F. Hohman, H. Kotek, H. G. Coleman, J. Li, J. Bigham, J. Cao, J. Lai, J. Cheung, J. Shan, J. Zhou, J. Li, J. Qin, K. Singh, K. Vega, K. Zou, L. Heckman, L. Gardiner, M. Bowler, M. Cordell, M. Cao, N. Hay, N. Shahdadpuri, O. Godwin, P. Dighe, P. Rachapudi, R. Tantawi, R. Frigg, S. Davarnia, S. Shah, S. Guha, S. Sirovica, S. Ma, S. Ma, S. Wang, S. Kim, S. Jayaram, V. Shankar, V. Paidi, V. Kumar, X. Wang, X. Zheng, W. Cheng, Y. Shrager, Y. Ye, Y. Tanaka, Y. Guo, Y. Meng, Z. T. Luo, Z. Ouyang, A. Aygar, A. Wan, A. Walkingshaw, A. Narayanan, A. Lin, A. Farooq, B. Ramerth, C. Reed, C. Bartels, C. Chaney, D. Riazati, E. L. Yang, E. Feldman, G. Hochstrasser, G. Seguin, I. Belousova, J. Pelemans, K. Yang, K. A. Vahid, L. Cao, M. Najibi, M. Zuliani, M. Horton, M. Cho, N. Bhendawade, P. Dong, P. Maj, P. Agrawal, Q. Shan, Q. Fu, R. Poston, S. Xu, S. Liu, S. Rao, T. Heeramun, T. Merth, U. Rayala, V. Cui, V. R. Sridhar, W. Zhang, W. Zhang, W. Wu, X. Zhou, X. Liu, Y. Zhao, Y. Xia, Z. Ren, and Z. Ren · 2024
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The n+ implementation details of RLHF with PPO: A case study on TL;DR summarization
Theoretical analysis of kl-regularized rlhf with multiple reference models, 2025
G. Aminian, A. R. Asadi, I. Shenfeld, and Y. Mroueh · 2025
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Deliberative alignment: Reasoning enables safer language models, 2025
M. Y. Guan, M. Joglekar, E. Wallace, S. Jain, B. Barak, A. Helyar, R. Dias, A. Vallone, H. Ren, J. Wei, H. W. Chung, S. Toyer, J. Heidecke, A. Beutel, and A. Glaese · 2025
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Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning
D. Guo, D. Yang, H. Zhang, J. Song, R. Zhang, R. Xu, Q. Zhu, S. Ma, P. Wang, X. Bi, et al · 2025
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Understanding r1-zero-like training: A critical perspective
Z. Liu, C. Chen, W. Li, P. Qi, T. Pang, C. Du, W. S. Lee, and M. Lin · 2025
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S. Huang, M. Noukhovitch, A. Hosseini, K. Rasul, W. Wang, and L. Tunstall · 2024
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Tülu 3: Pushing frontiers in open language model post-training
N. Lambert, J. Morrison, V. Pyatkin, S. Huang, H. Ivison, F. Brahman, L. J. V. Miranda, A. Liu, N. Dziri, S. Lyu, et al · 2024
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A. Liu, B. Feng, B. Xue, B. Wang, B. Wu, C. Lu, C. Zhao, C. Deng, C. Zhang, C. Ruan, et al · 2024
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Information theoretic guarantees for policy alignment in large language models, 2024
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Deepseekmath: Pushing the limits of mathematical reasoning in open language models
Z. Shao, P. Wang, Q. Zhu, R. Xu, J. Song, X. Bi, H. Zhang, M. Zhang, Y. Li, Y. Wu, et al · 2024
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Qwen2 Technical Report, Sept. 2024
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Trl: Transformer reinforcement learning
L. von Werra, Y. Belkada, L. Tunstall, E. Beeching, T. Thrush, N. Lambert, S. Huang, K. Rasul, and Q. Gallouédec
Cited in the paper.
Trl: Transformer reinforcement learning
L. von Werra, Y. Belkada, L. Tunstall, E. Beeching, T. Thrush, N. Lambert, S. Huang, K. Rasul, and Q. Gallouédec
Cited in the paper.
M. Luo, S. Tan, J. Wong, X. Shi, W. Y. Tang, M. Roongta, C. Cai, J. Luo, T. Zhang, L. E. Li, R. A. Popa, and I. Stoica · 2025
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What is the alignment objective of grpo?, 2025
M. Vojnovic and S.-Y. Yun · 2025
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Dapo: An open-source llm reinforcement learning system at scale, 2025
Q. Yu, Z. Zhang, R. Zhu, Y. Yuan, X. Zuo, Y. Yue, T. Fan, G. Liu, L. Liu, X. Liu, H. Lin, Z. Lin, B. Ma, G. Sheng, Y. Tong, C. Zhang, M. Zhang, W. Zhang, H. Zhu, J. Zhu, J. Chen, J. Chen, C. Wang, H. Yu, W. Dai, Y. Song, X. Wei, H. Zhou, J. Liu, W.-Y. Ma, Y.-Q. Zhang, L. Yan, M. Qiao, Y. Wu, and M. Wang · 2025
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