Abstract: Mean field games have been introduced to study games with a very large number of players. They combine mean field approximation techniques borrowed from statistical physics to describe the population and optimal control techniques to describe the behavior of a representative player. Mean field games and control problems have found many applications, particularly in economics and finance. Master equations are partial differential equations introduced by Pierre-Louis Lions to characterize Nash equilibria in such games. The unknown is a function taking the population distribution as an input, which is in general high dimensional. This motivates the investigation of deep learning methods for such equations. These methods typically rely on three ingredients: (1) representation of the distribution, (2) approximation of the function of interest, and (3) training algorithm. Since we cannot train on every possible distribution, the question of generalisation is unavoidable. In this respect, deep neural networks seem to be a promising tool. We will describe approaches that are based on the full knowledge of the model, as well as approaches that are model-free.

Bio: Mathieu Lauriere is currently an assistant professor of Mathematics and Data Science at NYU Shanghai. After obtaining his PhD from University Paris 7, he was a Postdoctoral Fellow at the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai and a Postdoctoral Research Associate at Princeton University, in the Operations Research and Financial Engineering (ORFE) department. Prior to his current position at NYU Shanghai, he was a Visiting Faculty Researcher at Google Brain, in the Brain Team (Paris).

His research interests include mean field control and mean field games, numerical methods, partial differential equations, stochastic analysis, machine learning, complexity theory, and quantum computing.

Meeting Recording: https://ucsb.zoom.us/rec/share/hjrS4Kl-6tfuGjaoVhFCKdKh891dWEPSqYqanGFuY-FL9kdTeaAEPNdBKAH5S9hd.HAlcB-CZBpeORni9

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