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

TL;DR

This paper introduces a no-regret learning algorithm using Gaussian processes to find Nash equilibria in black-box games where utility functions are unknown, with proven convergence and experimental validation.

Contribution

It presents a novel Gaussian process-based no-regret algorithm for learning Nash equilibria in black-box games, addressing a less-explored area.

Findings

The algorithm converges with a theoretical rate.

Effective in diverse game scenarios.

Validated through experiments.

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 the equilibrium 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.