Exploration noise for learning linear-quadratic mean field games

TL;DR

This paper shows that common noise can be used as an exploration mechanism in learning linear-quadratic mean field games, ensuring convergence of the fictitious play algorithm without additional structural assumptions.

Contribution

It demonstrates that common noise can serve as exploration noise in mean field games and guarantees convergence of learning algorithms in a simple linear-quadratic setting.

Findings

Common noise restores existence and uniqueness in the model.

Common noise ensures convergence of fictitious play.

Numerical examples support theoretical results.

Abstract

The goal of this paper is to demonstrate that common noise may serve as an exploration noise for learning the solution of a mean field game. This concept is here exemplified through a toy linear-quadratic model, for which a suitable form of common noise has already been proven to restore existence and uniqueness. We here go one step further and prove that the same form of common noise may force the convergence of the learning algorithm called `fictitious play', and this without any further potential or monotone structure. Several numerical examples are provided in order to support our theoretical analysis.