Speaker
Abstract
Optimal control problems arise broadly in science, engineering, and economics, but their numerical solution becomes challenging in high dimensions due to the curse of dimensionality and the nonlinear Hamilton–Jacobi–Bellman equation. In this talk, I will present a learning-based approach that brings ideas from reinforcement learning into continuous-time stochastic control. I will introduce an actor–critic framework in which the actor performs policy improvement through a policy-gradient flow, while the critic learns the value function using a variance-reduced temporal-difference formulation. Despite the nonconvex and coupled nature of the problem, we establish exponential convergence of the resulting single time-scale actor–critic flow. I will then extend this framework to mean field games by incorporating the evolution of the population distribution through an optimal-transport-based flow, leading to a unified mean field actor–critic method with convergence guarantees. Numerical examples illustrate the effectiveness of these methods for high-dimensional stochastic control and interacting-agent systems.
简介
周默，北京大学数学科学学院信息与计算科学系助理教授。2018年毕业于清华大学数学科学系。2023年获美国杜克大学（Duke University）数学博士学位，导师为鲁剑锋教授。随后在加州大学洛杉矶分校（UCLA）数学系担任博士后研究员，合作导师为Stanley Osher。2026年起在北京大学数学科学学院任助理教授。主要研究方向包括随机最优控制、平均场控制与平均场博弈、深度学习与生成模型，以及高维科学计算。