Learning in two-player zero-sum partially observable Markov games with perfect recall
Tadashi Kozuno, Pierre MENARD, Remi Munos, Michal Valko
Abstract
We study the problem of learning a Nash equilibrium (NE) in an extensive game with imperfect information (EGII) through self-play. Precisely, we focus on two-player, zero-sum, episodic, tabular EGII under the \textit{perfect-recall} assumption where the only feedback is realizations of the game (bandit feedback). In particular the \textit{dynamics of the EGII is not known}---we can only access it by sampling or interacting with a game simulator. For this learning setting, we provide the Implicit Exploration Online Mirror Descent (IXOMD) algorithm. It is a model-free algorithm with a high-probability bound on convergence rate to the NE of order $1/\sqrt{T}$ where~$T$ is the number of played games. Moreover IXOMD is computationally efficient as it needs to perform the updates only along the sampled trajectory.
BibTeX
@inproceedings{
kozuno2021learning,
title={Learning in two-player zero-sum partially observable Markov games with perfect recall},
author={Tadashi Kozuno and Pierre MENARD and Remi Munos and Michal Valko},
booktitle={Advances in Neural Information Processing Systems},
editor={A. Beygelzimer and Y. Dauphin and P. Liang and J. Wortman Vaughan},
year={2021},
url={https://openreview.net/forum?id=1LLemKrsgQp}
}