# Learning Two-Player Mixture Markov Games: Kernel Function Approximation and Correlated Equilibrium

arXiv: https://arxiv.org/abs/2208.05363 · HTML: https://mlsanity.com/paper/2208.05363/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 59 references that are in the map.
- First posted on arXiv 10 Aug 2022.

## Builds on (most cited first, 29 of 29)

- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Safe, Multi-Agent, Reinforcement Learning for Autonomous Driving](https://mlsanity.com/paper/1610.03295/) (2016)
- [Contextual Decision Processes with Low Bellman Rank are PAC-Learnable](https://mlsanity.com/paper/1610.09512/) (2016)
- [Model-Based Reinforcement Learning with Value-Targeted Regression](https://mlsanity.com/paper/2006.01107/) (2020)
- [Bellman Eluder Dimension: New Rich Classes of RL Problems, and Sample-Efficient Algorithms](https://mlsanity.com/paper/2102.00815/) (2021)
- [Generalization Bounds of Stochastic Gradient Descent for Wide and Deep Neural Networks](https://mlsanity.com/paper/1905.13210/) (2019)
- [Reinforcement Learning in Feature Space: Matrix Bandit, Kernels, and Regret Bound](https://mlsanity.com/paper/1905.10389/) (2019)
- [Nearly Minimax Optimal Reinforcement Learning for Linear Mixture Markov Decision Processes](https://mlsanity.com/paper/2012.08507/) (2020)
- [Learning Near Optimal Policies with Low Inherent Bellman Error](https://mlsanity.com/paper/2003.00153/) (2020)
- [Bilinear Classes: A Structural Framework for Provable Generalization in RL](https://mlsanity.com/paper/2103.10897/) (2021)
- [Model-based Reinforcement Learning and the Eluder Dimension](https://mlsanity.com/paper/1406.1853/) (2014)
- [V-Learning -- A Simple, Efficient, Decentralized Algorithm for Multiagent RL](https://mlsanity.com/paper/2110.14555/) (2021)
- [Provable Self-Play Algorithms for Competitive Reinforcement Learning](https://mlsanity.com/paper/2002.04017/) (2020)
- [Near-Optimal Reinforcement Learning with Self-Play](https://mlsanity.com/paper/2006.12007/) (2020)
- [A Sharp Analysis of Model-based Reinforcement Learning with Self-Play](https://mlsanity.com/paper/2010.01604/) (2020)
- [Provably Efficient Reinforcement Learning for Discounted MDPs with Feature Mapping](https://mlsanity.com/paper/2006.13165/) (2020)
- [Solving Linear Programs in the Current Matrix Multiplication Time](https://mlsanity.com/paper/1810.07896/) (2018)
- [Sample Complexity of Reinforcement Learning using Linearly Combined Model Ensembles](https://mlsanity.com/paper/1910.10597/) (2019)
- [Learning Zero-Sum Simultaneous-Move Markov Games Using Function Approximation and Correlated Equilibrium](https://mlsanity.com/paper/2002.07066/) (2020)
- [Online Reinforcement Learning in Stochastic Games](https://mlsanity.com/paper/1712.00579/) (2017)
- [The Power of Exploiter: Provable Multi-Agent RL in Large State Spaces](https://mlsanity.com/paper/2106.03352/) (2021)
- [Towards General Function Approximation in Zero-Sum Markov Games](https://mlsanity.com/paper/2107.14702/) (2021)
- [Solving Discounted Stochastic Two-Player Games with Near-Optimal Time and Sample Complexity](https://mlsanity.com/paper/1908.11071/) (2019)
- [Almost Optimal Algorithms for Two-player Zero-Sum Linear Mixture Markov Games](https://mlsanity.com/paper/2102.07404/) (2021)
- [Feature-Based Q-Learning for Two-Player Stochastic Games](https://mlsanity.com/paper/1906.00423/) (2019)
- [Learning Nash Equilibrium for General-Sum Markov Games from Batch Data](https://mlsanity.com/paper/1606.08718/) (2016)
- [On Reward-Free RL with Kernel and Neural Function Approximations: Single-Agent MDP and Markov Game](https://mlsanity.com/paper/2110.09771/) (2021)
- [Minimax Sample Complexity for Turn-based Stochastic Game](https://mlsanity.com/paper/2011.14267/) (2020)

## Built on by (most cited first, 1 of 1)

- [Double Pessimism is Provably Efficient for Distributionally Robust Offline Reinforcement Learning: Generic Algorithm and Robust Partial Coverage](https://mlsanity.com/paper/2305.09659/) (2023)

## Abstract (arXiv)

We consider learning Nash equilibria in two-player zero-sum Markov Games with nonlinear function approximation, where the action-value function is approximated by a function in a Reproducing Kernel Hilbert Space (RKHS). The key challenge is how to do exploration in the high-dimensional function space. We propose a novel online learning algorithm to find a Nash equilibrium by minimizing the duality gap. At the core of our algorithms are upper and lower confidence bounds that are derived based on the principle of optimism in the face of uncertainty. We prove that our algorithm is able to attain an O(√T) regret with polynomial computational complexity, under very mild assumptions on the reward function and the underlying dynamic of the Markov Games. We also propose several extensions of our algorithm, including an algorithm with Bernstein-type bonus that can achieve a tighter regret bound, and another algorithm for model misspecification that can be applied to neural function approximation.