A Bayesian Learning Algorithm for Unknown Zero-Sum Stochastic Games with an Arbitrary Opponent
Abstract
In this paper, we propose Posterior Sampling Reinforcement Learning for Zero-sum Stochastic Games (PSRL-ZSG), the first online learning algorithm that achieves Bayesian regret bound of $\tilde\mathcal{O}(HS\sqrt{AT})$ in the infinite-horizon zero-sum stochastic games with average-reward criterion. Here $H$ is an upper bound on the span of the bias function, $S$ is the number of states, $A$ is the number of joint actions and $T$ is the horizon. We consider the online setting where the opponent can not be controlled and can take any arbitrary time-adaptive history-dependent strategy. Our regret bound improves on the best existing regret bound of $\tilde\mathcal{O}(\sqrt[3]{DS^2AT^2})$ by Wei et al., (2017) under the same assumption and matches the theoretical lower bound in $T$.
Cite
Text
Jafarnia Jahromi et al. "A Bayesian Learning Algorithm for Unknown Zero-Sum Stochastic Games with an Arbitrary Opponent." Artificial Intelligence and Statistics, 2024.Markdown
[Jafarnia Jahromi et al. "A Bayesian Learning Algorithm for Unknown Zero-Sum Stochastic Games with an Arbitrary Opponent." Artificial Intelligence and Statistics, 2024.](https://mlanthology.org/aistats/2024/jafarniajahromi2024aistats-bayesian/)BibTeX
@inproceedings{jafarniajahromi2024aistats-bayesian,
title = {{A Bayesian Learning Algorithm for Unknown Zero-Sum Stochastic Games with an Arbitrary Opponent}},
author = {Jafarnia Jahromi, Mehdi and Jain, Rahul A and Nayyar, Ashutosh},
booktitle = {Artificial Intelligence and Statistics},
year = {2024},
pages = {3880-3888},
volume = {238},
url = {https://mlanthology.org/aistats/2024/jafarniajahromi2024aistats-bayesian/}
}