Mathematics & Machine Learning Seminar

Mean-field games (MFGs) provide elegant approximations to stochastic differential games with a large number of infinitesimal players and have become increasingly important in financial applications. In this talk, we introduce the mean-field actor-critic flow (MFAC), a reinforcement learning (RL)-based algorithm designed to solve MFGs, and establish its validity through both theoretical analysis and numerical experiments.

Unlike traditional RL approaches, our method employs partial differential equations (PDEs) to model the continuous-time training dynamics of the actor, critic, and population distribution. Inspired by optimal transport, the distributional dynamics evolve along a novel geodesic flow, and we prove convergence under a single time scale. Furthermore, borrowing ideas from generative modeling, we parameterize the distribution via score functions, the sampling from which is supported by Langevin Monte Carlo. Through numerical experiments, we demonstrate that MFAC effectively solves MFGs, achieving state-of-the-art performance.

This is joint work with Ruimeng Hu (UCSB) and Mo Zhou (UCLA)