# Offline Two-Player Zero-Sum Markov Games with KL Regularization

arXiv: https://arxiv.org/abs/2605.13025 · HTML: https://mlsanity.com/paper/2605.13025/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 52 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 30 of 44)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms](https://mlsanity.com/paper/1911.10635/) (2019)
- [Robust Adversarial Reinforcement Learning](https://mlsanity.com/paper/1703.02702/) (2017)
- [Is Pessimism Provably Efficient for Offline RL?](https://mlsanity.com/paper/2012.15085/) (2020)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [A Theory of Regularized Markov Decision Processes](https://mlsanity.com/paper/1901.11275/) (2019)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [Bellman-consistent Pessimism for Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06926/) (2021)
- [Self-Play Preference Optimization for Language Model Alignment](https://mlsanity.com/paper/2405.00675/) (2024)
- [Nash Learning from Human Feedback](https://mlsanity.com/paper/2312.00886/) (2023)
- [Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage](https://mlsanity.com/paper/2107.06226/) (2021)
- [Offline Reinforcement Learning with Realizability and Single-policy Concentrability](https://mlsanity.com/paper/2202.04634/) (2022)
- [V-Learning -- A Simple, Efficient, Decentralized Algorithm for Multiagent RL](https://mlsanity.com/paper/2110.14555/) (2021)
- [Near-Optimal Reinforcement Learning with Self-Play](https://mlsanity.com/paper/2006.12007/) (2020)
- [Exploratory Preference Optimization: Harnessing Implicit Q*-Approximation for Sample-Efficient RLHF](https://mlsanity.com/paper/2405.21046/) (2024)
- [A Sharp Analysis of Model-based Reinforcement Learning with Self-Play](https://mlsanity.com/paper/2010.01604/) (2020)
- [Settling the Sample Complexity of Model-Based Offline Reinforcement Learning](https://mlsanity.com/paper/2204.05275/) (2022)
- [Online Reinforcement Learning in Stochastic Games](https://mlsanity.com/paper/1712.00579/) (2017)
- [When Can We Learn General-Sum Markov Games with a Large Number of Players Sample-Efficiently?](https://mlsanity.com/paper/2110.04184/) (2021)
- [Online Iterative Reinforcement Learning from Human Feedback with General Preference Model](https://mlsanity.com/paper/2402.07314/) (2024)
- [Iterative Nash Policy Optimization: Aligning LLMs with General Preferences via No-Regret Learning](https://mlsanity.com/paper/2407.00617/) (2024)
- [Pessimistic Minimax Value Iteration: Provably Efficient Equilibrium Learning from Offline Datasets](https://mlsanity.com/paper/2202.07511/) (2022)
- [Provably Efficient Reinforcement Learning in Decentralized General-Sum Markov Games](https://mlsanity.com/paper/2110.05682/) (2021)

## Built on by (most cited first, 6 of 6)

- [Robust Data-Collection Policy Learning for Low-Variance Online Policy Evaluation](https://mlsanity.com/paper/2608.24146/) (2026)
- [OR-Transformer: Scaling Real-Time Decision-Making to 1,000 Items](https://mlsanity.com/paper/2609.01933/) (2026)
- [Learning to Sell: Reinforcement Learning for Strategic Large Language Model Agents in Multi-Product Markets](https://mlsanity.com/paper/2609.33289/) (2026)
- [Context-dependent agent evaluation with orthogonal equilibrium learning](https://mlsanity.com/paper/2609.31897/) (2026)
- [Pessimistic Minimax Learning for Public-Private Information Games under Unilateral Coverage](https://mlsanity.com/paper/2610.04997/) (2026)
- [Fast Rates for Offline Q-Learning with KL Regularization](https://mlsanity.com/paper/2610.18839/) (2026)

## Abstract (arXiv)

We study the problem of learning Nash equilibria in offline two-player zero-sum Markov games. While existing approaches often rely on explicit pessimism to address distribution shift, we show that KL regularization alone suffices to stabilize learning and guarantee convergence. We first introduce Regularized Offline Sequential Equilibrium (ROSE), a theoretical framework that achieves a fast widetildeO(1/n) convergence rate under textitunilateral concentrability, improving over the standard widetildeO(1/√n) rates in unregularized settings. We then propose Sequential Offline Self-play Mirror Descent (SOS-MD), a practical model-free algorithm based on least-squares value estimation and iterative self-play updates. We prove that the last iterate of SOS-MD attains the same widetildeO(1/n) statistical rate up to a vanishing optimization error of order widetildeO(1/√T) in the number of self-play iterations T.