Description
Lien visio : https://teams.microsoft.com/meet/338947823180486?p=AMcQfJfeL228rHWpve
Titre : On the convergence analysis of mirror descent method, which reveals the connection between Bregman divergence function and the Popov criterion.
Résumé : This talk presents a convergence analysis for the mirror descent (MD) method, a widely used algorithm in convex optimization. The key feature of this algorithm is that it provides a generalization of classical gradient-based methods via the use of generalized distance-like functions, which are formulated using the Bregman divergence. Via the framework of integral quadratic constraints (IQC), we show that the Bregman divergence from the optimal solution, which is commonly used as a Lyapunov function for this algorithm, is a special case of Lyapunov functions that follow when the Popov criterion is applied to an appropriate reformulation of the MD dynamics.
Biographie : Mengmou Li is currently a Tenure-Track Associate Professor at the Graduate School of Advanced Science and Engineering, Hiroshima University, Japan. He received the B.S. degree in Physics from Zhejiang University, China, in 2016, and the Ph.D. degree in Electrical and Electronic Engineering from The University of Hong Kong in 2020. He held postdoctoral positions at The Hong Kong University of Science and Technology, Hong Kong, the Control Group at the University of Cambridge, UK, and Tokyo Institute of Technology, Japan. His research interests include cyber-physical systems, optimization, and robust control.
