Computational mean-field games: from conventional methods to deep generative models

Data Science Seminar

Jiajia Yu (Duke University)

Abstract

Mean-field games study the behavior of a large number of rational agents in a non-cooperative game. It has wide applications in various fields. But it is not easy to solve the mean-field game numerically because of its complicated structure.

In the first part of my talk, I will present an efficient and flexible algorithm for dynamic mean-field games. The algorithm is based on an accelerated proximal gradient method. It consists of an easy-to-implement gradient descent step and a projection step equivalent to solving an elliptic equation. We also extend the setting of mean-field games and the algorithm to manifolds. In the second part of my talk, I will bridge mean-field games with a deep generative model which is called normalizing flows. The connection gives a computational approach for high-dimensional mean-field games and improves the training of the generative model.

The first part is based on joint works with Rongjie Lai (Purdue), Wuchen Li (UofSC) and Stanley Osher (UCLA). The second part is based on a joint work with Han Huang (RPI), Rongjie Lai (Purdue) and Jie Chen (IBM).