No-Regret Learning of Nash Equilibrium for Black-Box Games via Gaussian Processes

Minbiao Han, Fengxue Zhang, Yuxin Chen

Keywords: Nash Equilibrium, Game Theory, Gaussian Process

TL;DR: We study a no-regret learning algorithm using Gaussian processes to identify Nash equilibria in black-box games, validated theoretically and experimentally.

Abstract: This paper investigates the challenge of learning in black-box games, where the underlying utility function is unknown to any of the agents. While there is an extensive body of literature on the theoretical analysis of algorithms for computing the Nash equilibrium with *complete information* about the game, studies on Nash equilibrium in *black-box* games are less common. In this paper, we focus on learning the Nash equilibrium when the only available information about an agent's payoff comes in the form of empirical queries. We provide a no-regret learning algorithm that utilizes Gaussian processes to identify equilibria in such games. Our approach not only ensures a theoretical convergence rate but also demonstrates effectiveness across a variety collection of games through experimental validation.

List Of Authors: Han, Minbiao and Zhang, Fengxue and Chen, Yuxin

Code Url: https://github.com/SchroDeCat/UAI24-ARISE

Submission Number: 446