Generalized conditional gradient and learning in potential mean field games

TL;DR

This paper extends the conditional gradient algorithm to solve potential mean field games, demonstrating convergence rates and equivalence to fictitious play, with linear convergence under certain stepsize strategies.

Contribution

It introduces a generalized conditional gradient method for mean field games, establishing convergence properties and linking it to fictitious play.

Findings

The method converges with specific rates for different stepsize choices.

Linear convergence is achievable with line search stepsizes.

The algorithm is equivalent to fictitious play in this context.

Abstract

We investigate the resolution of second-order, potential, and monotone mean field games with the generalized conditional gradient algorithm, an extension of the Frank-Wolfe algorithm. We show that the method is equivalent to the fictitious play method. We establish rates of convergence for the optimality gap, the exploitability, and the distances of the variables to the unique solution of the mean field game, for various choices of stepsizes. In particular, we show that linear convergence can be achieved when the stepsizes are computed by linesearch.