Exploration Noise for Learning Linear-Quadratic Mean Field Games

• 成果类型: Article
• 署名作者: Delarue, Francois; Vasileiadis, Athanasios
• 署名单位: Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.0157
• 发表日期: 2025
• 关键词: partial-differential-equations; semi-lagrangian scheme; mckean-vlasov systems; numerical-methods; CONVERGENCE; algorithms; uniqueness; approximation; cubature; fbsdes

摘要

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.