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SUMMARY:TILOS Seminar: Non-convex Optimization for Linear Quadratic Gaussian (LQG) Control
DESCRIPTION:Yang Zheng\, Assistant Professor\, UC San Diego \nAbstract: 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.
URL:https://tilos.ai/event/tilos-seminar-non-convex-optimization-for-linear-quadratic-gaussian-lqg-control/
LOCATION:Virtual
CATEGORIES:TILOS Seminar Series
ATTACH;FMTTYPE=image/jpeg:https://tilos.ai/wp-content/uploads/2023/09/zheng-yang-e1757006534476.jpg
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DTSTART;TZID=America/Los_Angeles:20220928T100000
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CREATED:20250904T172904Z
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UID:7355-1664359200-1664362800@tilos.ai
SUMMARY:TILOS Seminar: On Policy Optimization Methods for Control
DESCRIPTION:Maryam Fazel\, Professor\, University of Washington \nAbstract: Policy Optimization methods enjoy wide practical use in reinforcement learning (RL) for applications ranging from robotic manipulation to game-playing\, partly because they are easy to implement and allow for richly parameterized policies. Yet their theoretical properties\, from optimality to statistical complexity\, are still not fully understood. To help develop a theoretical basis for these methods\, and to bridge the gap between RL and control theoretic approaches\, recent work has studied whether gradient-based policy optimization can succeed in designing feedback control policies. In this talk\, we start by showing the convergence and optimality of these methods for linear dynamical systems with quadratic costs\, where despite nonconvexity\, convergence to the optimal policy occurs under mild assumptions. Next\, we make a connection between convex parameterizations in control theory on one hand\, and the Polyak-Lojasiewicz property of the nonconvex cost function\, on the other. Such a connection between the nonconvex and convex landscapes provides a unified view towards extending the results to more complex control problems.
URL:https://tilos.ai/event/tilos-seminar-on-policy-optimization-methods-for-control/
LOCATION:Virtual
CATEGORIES:TILOS Seminar Series
ATTACH;FMTTYPE=image/jpeg:https://tilos.ai/wp-content/uploads/2023/10/fazel-maryam.jpg
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