TILOS Seminar: Non-convex Optimization for Linear Quadratic Gaussian (LQG) Control
Yang Zheng, Assistant Professor, UC San Diego
Recent studies have started to apply machine learning techniques to the control of unknown dynamical systems. They have achieved impressive empirical results. However, the convergence behavior, statistical properties, and robustness performance of these approaches are often poorly understood due to the non-convex nature of the underlying control problems. In this talk, we revisit the Linear Quadratic Gaussian (LQG) control and present recent progress towards its landscape analysis from a non-convex optimization perspective. We view the LQG cost as a function of the controller parameters and study its analytical and geometrical properties. Due to the inherent symmetry induced by similarity transformations, the LQG landscape is very rich yet complicated. We show that 1) the set of stabilizing controllers has at most two path-connected components, and 2) despite the nonconvexity, all minimal stationary points (controllable and observable controllers) are globally optimal. Based on the special non-convex optimization landscape, we further introduce a novel perturbed policy gradient (PGD) method to escape a large class of suboptimal stationary points (including high-order saddles). These results shed some light on the performance analysis of direct policy gradient methods for solving the LQG problem. The talk is based on our recent papers: https://arxiv.org/abs/2102.04393 and https://arxiv.org/abs/2204.00912.
Yang Zheng is an assistant professor in the ECE department at UC San Diego. Yang Zheng received the DPhil (Ph.D.) degree in Engineering Science from the University of Oxford in 2019. He received the B.E. and M.S. degrees from Tsinghua University in 2013 and 2015, respectively. From February 2019 to August 2020, he was a postdoctoral researcher at Harvard University. He was a research associate at Imperial College London in 2021.
Dr. Zheng’s research interests include learning, optimization, and control of network systems, and their applications to cyber-physical systems, autonomous vehicles, and traffic systems. His work has been acknowledged by several awards, including the 2019 European Ph.D. Award on Control for Complex and Heterogeneous Systems, the Best Student Paper Award Finalist at the 2019 European Control Conference, the Best Student Paper Award at the 17th IEEE International Conference on Intelligent Transportation Systems, and the Best Paper Award at the 14th Intelligent Transportation Systems Asia-Pacific Forum. He received the National Scholarship, Outstanding Graduate at Tsinghua University, the Clarendon Scholarship at the University of Oxford, and the Chinese Government Award for Outstanding Self-financed Students Abroad.
