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Reinforcement learning (RL) has emerged as a powerful method for improving the reasoning abilities of large language models (LLMs).
Randomized algorithms
Rajeev Motwani and Prabhakar Raghavan · 1996
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Finite-time analysis of the multiarmed bandit problem
Peter Auer, Nicolo Cesa-Bianchi, and Paul Fischer · 2002
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R-max-a general polynomial time algorithm for near-optimal reinforcement learning
Ronen I Brafman and Moshe Tennenholtz · 2002
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Near-optimal reinforcement learning in polynomial time
Michael Kearns and Satinder Singh · 2002
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(more) efficient reinforcement learning via posterior sampling
Ian Osband, Daniel Russo, and Benjamin Van Roy · 2013
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Learning to optimize via posterior sampling
Daniel Russo and Benjamin Van Roy · 2014
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Unifying count-based exploration and intrinsic motivation
Marc Bellemare, Sriram Srinivasan, Georg Ostrovski, Tom Schaul, David Saxton, and Remi Munos · 2016
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PAC reinforcement learning with rich observations
Akshay Krishnamurthy, Alekh Agarwal, and John Langford · 2016
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Deep exploration via bootstrapped dqn
Ian Osband, Charles Blundell, Alexander Pritzel, and Benjamin Van Roy · 2016
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Minimax regret bounds for reinforcement learning
Mohammad Gheshlaghi Azar, Ian Osband, and Rémi Munos · 2017
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Contextual decision processes with low Bellman rank are PAC-learnable
Nan Jiang, Akshay Krishnamurthy, Alekh Agarwal, John Langford, and Robert E Schapire · 2017
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Exploration by random network distillation
Yuri Burda, Harrison Edwards, Amos Storkey, and Oleg Klimov · 2018
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Is q-learning provably efficient?
Chi Jin, Zeyuan Allen-Zhu, Sebastien Bubeck, and Michael I Jordan · 2018
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Learning to optimize via information-directed sampling
Daniel Russo and Benjamin Van Roy · 2018
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Sample-optimal parametric Q-learning using linearly additive features
Lin Yang and Mengdi Wang · 2019
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Model-based reinforcement learning with value-targeted regression
Alex Ayoub, Zeyu Jia, Csaba Szepesvari, Mengdi Wang, and Lin Yang · 2020
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Provably efficient reinforcement learning with linear function approximation
Chi Jin, Zhuoran Yang, Zhaoran Wang, and Michael I Jordan · 2020
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No-regret exploration in contextual reinforcement learning
Aditya Modi and Ambuj Tewari · 2020
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Approximating kl divergence, 2020
John Schulman · 2020
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Bilinear classes: A structural framework for provable generalization in RL
Simon S Du, Sham M Kakade, Jason D Lee, Shachar Lovett, Gaurav Mahajan, Wen Sun, and Ruosong Wang · 2021
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The statistical complexity of interactive decision making
Dylan J Foster, Sham M Kakade, Jian Qian, and Alexander Rakhlin · 2021
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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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PC-MLP: Model-based reinforcement learning with policy cover guided exploration
Yuda Song and Wen Sun · 2021
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Nearly minimax optimal reinforcement learning for linear mixture markov decision processes
Dongruo Zhou, Quanquan Gu, and Csaba Szepesvari · 2021
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Training a helpful and harmless assistant with reinforcement learning from human feedback
Yuntao Bai, Andy Jones, Kamal Ndousse, Amanda Askell, Anna Chen, Nova DasSarma, Dawn Drain, Stanislav Fort, Deep Ganguli, Tom Henighan, et al · 2022
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Training language models to follow instructions with human feedback
Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, et al · 2022
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Vo q q l: Towards optimal regret in model-free rl with nonlinear function approximation
Alekh Agarwal, Yujia Jin, and Tong Zhang · 2023
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Asymmetric reinforce for off-policy reinforcement learning: Balancing positive and negative rewards
Charles Arnal, GaĂŤtan Narozniak, Vivien Cabannes, Yunhao Tang, Julia Kempe, and Remi Munos · 2025
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Online preference alignment for language models via count-based exploration
Chenjia Bai, Yang Zhang, Shuang Qiu, Qiaosheng Zhang, Kang Xu, and Xuelong Li · 2025
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Pass@ k training for adaptively balancing exploration and exploitation of large reasoning models
Zhipeng Chen, Xiaobo Qin, Youbin Wu, Yue Ling, Qinghao Ye, Wayne Xin Zhao, and Guang Shi · 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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Understanding the effects of rlhf on llm generalisation and diversity
Robert Kirk, Ishita Mediratta, Christoforos Nalmpantis, Jelena Luketina, Eric Hambro, Edward Grefenstette, and Roberta Raileanu · 2023
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Let’s verify step by step
Hunter Lightman, Vineet Kosaraju, Yuri Burda, Harrison Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe · 2023
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Direct preference optimization: Your language model is secretly a reward model
Rafael Rafailov, Archit Sharma, Eric Mitchell, Christopher D Manning, Stefano Ermon, and Chelsea Finn · 2023
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Wei Xiong, Hanze Dong, Chenlu Ye, Ziqi Wang, Han Zhong, Heng Ji, Nan Jiang, and Tong Zhang · 2023
Cited alongside, same era.
Principled reinforcement learning with human feedback from pairwise or k-wise comparisons
Banghua Zhu, Michael Jordan, and Jiantao Jiao · 2023
Cited alongside, same era.
A general theoretical paradigm to understand learning from human preferences
Mohammad Gheshlaghi Azar, Zhaohan Daniel Guo, Bilal Piot, Remi Munos, Mark Rowland, Michal Valko, and Daniele Calandriello · 2024
Cited alongside, same era.
Value-incentivized preference optimization: A unified approach to online and offline rlhf
Shicong Cen, Jincheng Mei, Katayoon Goshvadi, Hanjun Dai, Tong Yang, Sherry Yang, Dale Schuurmans, Yuejie Chi, and Bo Dai · 2024
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Xingyu Dang, Christina Baek, Kaiyue Wen, Zico Kolter, and Aditi Raghunathan · 2025
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Navigate the unknown: Enhancing llm reasoning with intrinsic motivation guided exploration
Jingtong Gao, Ling Pan, Yejing Wang, Rui Zhong, Chi Lu, Qingpeng Cai, Peng Jiang, and Xiangyu Zhao · 2025
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Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning
Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Ruoyu Zhang, Runxin Xu, Qihao Zhu, Shirong Ma, Peiyi Wang, Xiao Bi, et al · 2025
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Diverse preference optimization
Jack Lanchantin, Angelica Chen, Shehzaad Dhuliawala, Ping Yu, Jason Weston, Sainbayar Sukhbaatar, and Ilia Kulikov · 2025
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Jointly reinforcing diversity and quality in language model generations
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Antoine Moulin, Gergely Neu, and Luca Viano · 2025
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e3: Learning to explore enables extrapolation of test-time compute for llms
Amrith Setlur, Matthew YR Yang, Charlie Snell, Jeremy Greer, Ian Wu, Virginia Smith, Max Simchowitz, and Aviral Kumar · 2025
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Can large reasoning models self-train?
Sheikh Shafayat, Fahim Tajwar, Ruslan Salakhutdinov, Jeff Schneider, and Andrea Zanette · 2025
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Training a generally curious agent
Fahim Tajwar, Yiding Jiang, Abitha Thankaraj, Sumaita Sadia Rahman, J Zico Kolter, Jeff Schneider, and Ruslan Salakhutdinov · 2025
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On a few pitfalls in kl divergence gradient estimation for rl
Yunhao Tang and Rémi Munos · 2025
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Optimizing language models for inference time objectives using reinforcement learning
Yunhao Tang, Kunhao Zheng, Gabriel Synnaeve, and Rémi Munos · 2025
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The invisible leash: Why rlvr may not escape its origin
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Dapo: An open-source llm reinforcement learning system at scale
Qiying Yu, Zheng Zhang, Ruofei Zhu, Yufeng Yuan, Xiaochen Zuo, Yu Yue, Weinan Dai, Tiantian Fan, Gaohong Liu, Lingjun Liu, et al · 2025
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Does reinforcement learning really incentivize reasoning capacity in llms beyond the base model?
Yang Yue, Zhiqi Chen, Rui Lu, Andrew Zhao, Zhaokai Wang, Shiji Song, and Gao Huang · 2025
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The price of format: Diversity collapse in llms
Longfei Yun, Chenyang An, Zilong Wang, Letian Peng, and Jingbo Shang · 2025
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Echo chamber: Rl post-training amplifies behaviors learned in pretraining
Rosie Zhao, Alexandru Meterez, Sham Kakade, Cengiz Pehlevan, Samy Jelassi, and Eran Malach · 2025
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First return, entropy-eliciting explore
Tianyu Zheng, Tianshun Xing, Qingshui Gu, Taoran Liang, Xingwei Qu, Xin Zhou, Yizhi Li, Zhoufutu Wen, Chenghua Lin, Wenhao Huang, et al · 2025
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