暗网禁区 学术报告[2026]079号

（高水平大学建设系列报告1338号）

报告题目：Some Theoretical Foundations of Exploratory Time-inconsistent Control Problems

报告人：余翔 副教授 （香港理工大学）

报告时间：2026年7月22日15:00-16:00

报告地点：深圳大学粤海校区汇星楼514会议室

报告摘要：We investigate two core theoretical foundations of the exploratory reinforcement learning for time-inconsistent control problems under entropy regularization. In the first part, for a fixed entropy regularization, we propose a policy iteration algorithm (PIA) and establish its convergence to a regularized equilibrium policy. The design of the PIA is based on a coupled system of non-local partial differential equations, called the exploratory equilibrium Hamilton--Jacobi--Bellman (EEHJB) equation. As opposed to the standard time-consistent case, policy improvement fails. To overcome this issue, we prove that the value functions generated by the PIA form a Cauchy sequence in a specialized Banach space, hence admit a limit, and the rate of convergence is exponential, on the strength of the Bismut--Elworthy--Li formula of stochastic representation. The limiting value function is shown to satisfy the EEHJB equation, which induces a regularized equilibrium in a Gibbs form. In the second part, we show that the classical solution of the EEHJB converges to a strong solution of the original equilibrium HJB (EHJB) equation as entropy regularization vanishes, which further implies that the regularized equilibrium converges to the equilibrium in the original time-inconsistent control problem. As an important by-product, we establish the existence of equilibrium in the diffusion model under time-inconsistency without resorting to strong regularity assumptions as in the literature.

报告人简介： Prof. Xiang Yu is currently an Associate Professor in the Department of Applied Mathematics at the Hong Kong Polytechnic University. He obtained his Ph.D. degree in Mathematics from the University of Texas at Austin in 2012. His research interests lie at the intersection of quantitative finance, stochastic control, reinforcement learning, mean-field control and games. He has extensive publications in Annals of Applied Probability, Mathematical Finance, Finance and Stochastics, Mathematics of Operations Research, SIAM Journal on Control and Optimization, SIAM Journal on Financial Mathematics, Stochastic Processes and their Applications, Automatica, etc.

邀请人：王寒霄

暗网禁区

2026年7月17日