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We provide a theoretical framework for Reinforcement Learning with Human Feedback (RLHF). Our analysis shows that when the true reward function is linear, the widely used maximum likelihood estimator (MLE) converges under both the…

Machine Learning · Computer Science 2024-02-09 Banghua Zhu , Jiantao Jiao , Michael I. Jordan

We study online optimization methods for zero-sum games, a fundamental problem in adversarial learning in machine learning, economics, and many other domains. Traditional methods approximate Nash equilibria (NE) using either regret-based…

Computer Science and Game Theory · Computer Science 2025-07-16 Taemin Kim , James P. Bailey

This paper studies reinforcement learning from human feedback (RLHF) for aligning large language models with human preferences. While RLHF has demonstrated promising results, many algorithms are highly sensitive to misspecifications in the…

Machine Learning · Computer Science 2025-10-30 Erhan Xu , Kai Ye , Hongyi Zhou , Luhan Zhu , Francesco Quinzan , Chengchun Shi

Aligning large language models (LLMs) to serve users with heterogeneous and potentially conflicting preferences is a central challenge for personalized and trustworthy AI. We formalize an ideal notion of universal alignment through…

Machine Learning · Computer Science 2026-01-14 Yang Cai , Weiqiang Zheng

We study the problem of repeated play in a zero-sum game in which the payoff matrix may change, in a possibly adversarial fashion, on each round; we call these Online Matrix Games. Finding the Nash Equilibrium (NE) of a two player zero-sum…

Machine Learning · Computer Science 2020-04-06 Adrian Rivera Cardoso , Jacob Abernethy , He Wang , Huan Xu

We study the problem of learning in zero-sum matrix games with repeated play and bandit feedback. Specifically, we focus on developing uncoupled algorithms that guarantee, without communication between players, the convergence of the…

Machine Learning · Computer Science 2026-04-20 Côme Fiegel , Pierre Ménard , Tadashi Kozuno , Michal Valko , Vianney Perchet

Human preference alignment is essential to improve the interaction quality of large language models (LLMs). Existing alignment methods depend on manually annotated preference data to guide the LLM optimization directions. However,…

Computation and Language · Computer Science 2024-06-04 Pengyu Cheng , Yifan Yang , Jian Li , Yong Dai , Tianhao Hu , Peixin Cao , Nan Du , Xiaolong Li

Reinforcement learning from human feedback (RLHF) has emerged as a key technique for aligning the output of large language models (LLMs) with human preferences. To learn the reward function, most existing RLHF algorithms use the…

Machine Learning · Statistics 2026-02-11 Kai Ye , Hongyi Zhou , Jin Zhu , Francesco Quinzan , Chengchun Shi

This work studies the challenge of aligning large language models (LLMs) with offline preference data. We focus on alignment by Reinforcement Learning from Human Feedback (RLHF) in particular. While popular preference optimization methods…

Machine Learning · Computer Science 2024-06-07 Xiang Ji , Sanjeev Kulkarni , Mengdi Wang , Tengyang Xie

Bargaining games, where agents attempt to agree on how to split utility, are an important class of games used to study economic behavior, which motivates a study of online learning algorithms in these games. In this work, we tackle when…

Computer Science and Game Theory · Computer Science 2025-07-08 Serafina Kamp , Reese Liebman , Benjamin Fish

A key challenge in training Large Language Models (LLMs) is properly aligning them with human preferences. Reinforcement Learning with Human Feedback (RLHF) uses pairwise comparisons from human annotators to train reward functions and has…

Machine Learning · Computer Science 2025-01-17 Ariel D. Procaccia , Benjamin Schiffer , Shirley Zhang

Despite notable advancements in Multimodal Large Language Models (MLLMs), most state-of-the-art models have not undergone thorough alignment with human preferences. This gap exists because current alignment research has primarily achieved…

Learning from human feedback (LHF) -- and in particular learning from pairwise preferences -- has recently become a crucial ingredient in training large language models (LLMs), and has been the subject of much research. Most recent works…

Machine Learning · Computer Science 2024-01-11 Vincent Dumoulin , Daniel D. Johnson , Pablo Samuel Castro , Hugo Larochelle , Yann Dauphin

While extensive-form games (EFGs) can be converted into normal-form games (NFGs), doing so comes at the cost of an exponential blowup of the strategy space. So, progress on NFGs and EFGs has historically followed separate tracks, with the…

Computer Science and Game Theory · Computer Science 2022-02-02 Gabriele Farina , Chung-Wei Lee , Haipeng Luo , Christian Kroer

Aligning the behavior of Large language models (LLMs) with human intentions and values remains a critical challenge. Reinforcement learning from human feedback (RLHF) aligns LLMs by training a reward model (RM) on human preferences and…

Computation and Language · Computer Science 2025-12-25 Jiayi Zhou , Jiaming Ji , Juntao Dai , Dong Li , Yaodong Yang

Reinforcement learning from human feedback (RLHF) is a prevalent approach to align AI systems with human values by learning rewards from human preference data. Due to various reasons, however, such data typically takes the form of rankings…

Machine Learning · Computer Science 2024-06-06 Ilgee Hong , Zichong Li , Alexander Bukharin , Yixiao Li , Haoming Jiang , Tianbao Yang , Tuo Zhao

We present volume analyses of Multiplicative Weights Updates (MWU) and Optimistic Multiplicative Weights Updates (OMWU) in zero-sum as well as coordination games. Such analyses provide new insights into these game dynamical systems, which…

Computer Science and Game Theory · Computer Science 2020-05-29 Yun Kuen Cheung , Georgios Piliouras

We prove that optimistic-follow-the-regularized-leader (OFTRL), together with smooth value updates, finds an $O(T^{-1})$-approximate Nash equilibrium in $T$ iterations for two-player zero-sum Markov games with full information. This…

Machine Learning · Computer Science 2023-02-10 Yuepeng Yang , Cong Ma

Reinforcement Learning from Human Feedback (RLHF) is crucial for aligning Large Language Models (LLMs) with human values. However, RLHF has been continuously challenged by its high complexity in implementation and computation consumption,…

Machine Learning · Computer Science 2026-03-24 Yuhao Du , Zhuo Li , Pengyu Cheng , Zhihong Chen , Yuejiao Xie , Xiang Wan , Anningzhe Gao

Learning from repeated play in a fixed two-player zero-sum game is a classic problem in game theory and online learning. We consider a variant of this problem where the game payoff matrix changes over time, possibly in an adversarial…

Machine Learning · Computer Science 2022-02-01 Mengxiao Zhang , Peng Zhao , Haipeng Luo , Zhi-Hua Zhou