Abstract: Mean field games (MFG) and mean field control (MFC) describe the behavior of agents interacting in a symmetric fashion when the number of agents grows to infinity. The first theory captures a notion of Nash equilibrium for selfish players while the second one focuses on the notion of social cost for cooperative agents. In this talk, we present several numerical methods based on machine learning for these problems. Relying either on a partial differential equation (PDE) viewpoint or on a forward-backward stochastic differential equation (FBSDE) viewpoint, we tackle both the ergodic and the finite time horizon settings. Using results from the theory of approximation by neural networks, we provide rigorous guarantees on the convergence rate of our numerical schemes. If time permits, we will also discuss extensions to model-free algorithms based on reinforcement learning.

Bio: Mathieu Laurière is a Postdoctoral Research Associate at Princeton University, in the Operations Research and Financial Engineering (ORFE) department. He obtained his MS from University Paris 6 and ENS Cachan, and his PhD from University Paris 7. Prior to joining Princeton University, he was a Postdoctoral Fellow at the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai. His research interests include mean-field control and games, numerical methods and machine learning.