Title:

Actor-critic method for solving high dimensional Hamilton-Jacobi-Bellman type PDEs 

Abstract:

In this talk, we will discuss numerical approach to solve high dimensional Hamilton-Jacobi-Bellman (HJB) type partial differential equations (PDEs). 

The HJB PDEs, reformulated as optimal control problems, are tackled by the actor-critic framework inspired by reinforcement learning, based on neural network parametrization of the value and control functions. Within the actor-critic framework, we employ a policy gradient approach to improve the control, while for the value function, we derive a variance reduced least-squares temporal difference method using stochastic calculus. We will also discuss convergence analysis for the actor-critic method, in particular the policy gradient method for solving stochastic optimal control. Joint work with Jiequn Han (Flatiron Institute) and Mo Zhou (Duke University).

Bio:

Jianfeng Lu is a Professor of Mathematics, Physics, and Chemistry at Duke University. Before joining Duke University, he obtained his PhD in Applied Mathematics from Princeton University in 2009 and was a Courant Instructor at New York University from 2009 to 2012. He works on mathematical analysis and algorithm development for problems and challenges arising from computational physics, theoretical chemistry, materials science, high-dimensional PDEs, and machine learning. He is a fellow of AMS. His work has been recognized by a Sloan Fellowship, a NSF Career Award, the IMA Prize in Mathematics and its Applications, and the Feng Kang Prize.