Thesis Defenses Seminar
Monday, April 3, 2023, 11:00am, 359 Gross Hall
Mo Zhou (Duke University, Mathematics)
Deep Learning Method for Partial Differential Equations and Optimal Problems
The stochastic optimal control problem and the corresponding Hamilton—Jacobi—Bellman (HJB) equation is hard to solve due to its complexity and non-convexity. We propose an actor-critic method to solve the optimal control. We derive an explicit derivative for the cost functional and propose a policy gradient method for the actor (control) update. This derivative requires the value function for the current control, so we develop a policy evaluation process for the critic. We show that the both the actor and the critic have exponential convergence rates under mild assumptions. Moreover, we also show such rate for the joint actor-critic dynamic with single time scale.

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