Generalized conditional gradient and learning in potential mean field games

Pierre Lavigne (1) , Laurent Pfeiffer (2, 3)

1 Institut Louis Bachelier
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
3 L2S - Laboratoire des signaux et systèmes

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.

Mots clés: Learning; Exploitability; Line search; Mean field games; Generalized conditional gradient; Fictitious play

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Pierre Lavigne, Laurent Pfeiffer. Generalized conditional gradient and learning in potential mean field games. Applied Mathematics and Optimization, 2023, 88, ⟨10.1007/s00245-023-10056-8⟩. ⟨hal-03341776v3⟩