Exploration Noise for Learning Linear-Quadratic Mean Field Games

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 to support our theoretical analysis.Funding: F. Delarue acknowledges the financial support of the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme [AdG ELISA project, Grant 101054746]. A. Vasileiadis acknowledge the financial support of French ANR project ANR-19-P3IA-0002-3IA Côte d'Azur-Nice-Interdisciplinary Institute for Artificial Intelligence.