This was part of Mathematical Advances in Mean Field Games
Computational Methods in High-Dimensional Stochastic Optimal Control
Mete Soner, Princeton University
Monday, December 13, 2021
Abstract: McKean-Vlasov control problems are naturally formulated in the infinite-dimensional Wasserstein spaces. Their effective approximations are therefore high-dimensional and until recently such problems were essentially intractable. However, several recent studies report impressive numerical results in quite high dimensions. All these papers use a Monte-Carlo type algorithm combined with deep neural networks proposed by Han, E and Jentzen. In this talk I will outline this approach and discuss its properties. Numerical results, while validating the power of the method in high dimensions, it also show the dependence of the dimension and the size of the training data. This is joint work with Max Reppen of Boston University and Valentin Tissot-Daguette from Princeton.