The development of deep learning has provided us new powerful tools to solve high-dimensional problems. This talk will start with a control-viewpoint of deep learning, discussing the connection between optimizing neural networks and solving optimal control problems. Inspired by such a connection, we will present two lines of research that leverage deep learning to solve high-dimensional control problems: (1) solving stochastic control problems, with possible delay effect; (2) solving parabolic PDEs based on backward stochastic differential equations (BSDE). The numerical results suggest that the proposed algorithms achieve satisfactory accuracy and, at the same time, can handle rather high-dimensional problems. This opens up new possibilities in economics, finance, and operational research, by considering more realistic and informative high-dimensional states.
Speaker: Dr Jiequn Han
Date: 10 November 2021 (Wednesday)
Time: 10:00am – 11:00am
Poster: Click here
Dr Jiequn Han is a Research Fellow in the Center for Computational Mathematics, Flatiron Institute. Previously, he worked as an Instructor in the Department of Mathematics at Princeton University. His research draws inspiration from various disciplines of science and is devoted to solving high-dimensional problems arising from scientific computing. His current research interests mainly focus on solving high-dimensional partial differential equations and machine learning based-multiscale modeling. He holds a Ph.D. in Applied Mathematics from Princeton University, a B.S. in Computational Mathematics and a B.A. in Economics from Peking University.