勷勤数学•专家报告

题      目：Hamilton-Jacobi-Bellman equations and controlled particle systems for generalized mean field control

报  告  人： 廖华夫 教授  (邀请人：杨舟)

                                   大连理工大学

时      间： 6月14日  10：00-11:00

地     点：数科院西楼二楼会议室

报告人简介:

       廖华夫，教授、博士生导师，2019年博士毕业于中国科学技术大学，曾先后在新加坡国立大学、柏林洪堡大学、香港城市大学从事博士后研究，之后于2024年加入大连理工大学。主要研究兴趣为随机最优控制理论及其在数理金融和机器学习中的应用，围绕相关问题已在 Ann. Appl. Probab., SIAM J. Control Optim., Math. Financ. Econ.等学术期刊上发表多篇论文。

摘      要：

       In this talk I will present some of our recent works on HJB equations for generalized mean field control (MFC) and related controlled N-particle systems. Such kind of HJB equations are nonlinearly coupled with the distribution induced by the Wasserstein derivatives of solutions. A typical example of this kind of HJB equations arises from the mean field limit of controlled particle systems for neural SDE. A local in time classical solution for the HJB equation is generated via a probabilistic approach based on the mean field maximum principle. Given an extension of the displacement convexity condition, we obtain the uniform estimates on the HJB equation for the N-particle system. Thanks to the local well-posedness and the uniform estimates, we prove the global well-posedness of HJB equations for generalized MFC, which is also true for the degenerated case. I will also talk about related topics including Lipschitz approximators to optimal feedback functions for generalized MFC. This talk is based on joint works with Alpár R. Mészáros, Chenchen Mou and Chao Zhou.

          欢迎老师、同学们参加、交流！