Sharp propagation of chaos for mean field Langevin dynamics, control, and games

TL;DR

This paper proves the optimal rate at which systems of particles approximate mean field models, with applications to mean field games, control, and Langevin dynamics, using advanced hierarchical and chaos propagation techniques.

Contribution

It establishes the sharp propagation of chaos rates for non-linear McKean-Vlasov equations, including uniform-in-time results for Langevin dynamics in convex regimes.

Findings

Optimal propagation of chaos rates for McKean-Vlasov equations.

Uniform-in-time convergence results for Langevin dynamics.

Application to mean field games and control problems.

Abstract

We establish the sharp rate of propagation of chaos for McKean-Vlasov equations with coefficients that are non-linear in the measure argument, i.e., not necessarily given by pairwise interactions. Results are given both on bounded time horizon and uniform in time. As applications, we deduce the sharp rate of propagation of chaos for the convergence problem in mean field games and control, and for mean field Langevin dynamics, the latter being uniform in time in the strongly displacement convex regime. Our arguments combine the BBGKY hierarchy with techniques from the literature on weak propagation of chaos.