报告题目 (Title)：Value-Gradient Formulation for Optimal Control Problem and its Machine-Learning Algorithm
报告人 (Speaker)： 周翔 教授（香港城市大学）
报告时间 (Time)：2021年11月25日(周四) 10:30
报告地点 (Place)：G507
邀请人(Inviter)：余长君
主办部门：理学院数学系
报告摘要：Optimal control problem is typically cast as a nonlinear Hamiltonian-Jacobi-Bellman PDE problem which the value function satisfies. In this talk, we show motivations of focusing its gradient and derive a PDE system for the (vector-valued) gradient of the value function (value-gradient function), which is closed and enjoys a nice component-decoupling property. This PDE system of value-gradient can be solved by the method of characteristics as the linear HJB equation: one curve of characteristics will produce the data for both value and value-gradient. Supplemented by this additional value-gradient data, the value function is then computed by minimizing the sum of two mean square errors between the data and the parametric function approximations. We show by a few numerical examples the improvement of both robustness and accuracy when such value-gradient is taken into account. The linear convergence of the iterative algorithm is proved under mild conditions. This is joint work with A. Bensoussan and P. Yam and JY Han.
