November 20, 2024

We will have a technical talk this Friday. Spencer Kraisler, a PhD candidate from Prof. Mehran Mesbahi’s group, will give a talk on his latest work “LQG Controller Synthesis through Riemannian Optimization: Orbits and Quotient Manifolds” submitted to CDC 2024. The talk is a continuation from last week Mehran’s talk and there will be food!

📅 Date: Friday Nov 22
🕕 Time: 12:30PM – 1:30PM(ish)

🏛️ Location: SIG 224
💻 Zoom: Zoom Link

Title: LQG Controller Synthesis through Riemannian Optimization: Orbits and Quotient Manifolds

Abstract: We consider direct policy optimization for the linear-quadratic Gaussian (LQG) setting. Over the past few years, it has been recognized that the landscape of dynamic output-feedback controllers of relevance to LQG has an intricate geometry, particularly pertaining to the existence of degenerate stationary points, that hinders gradient methods. In order to address these challenges, in this letter, we adopt a system-theoretic coordinate-invariant Riemannian metric for the space of dynamic output-feedback controllers and develop a Riemannian gradient descent for direct LQG policy optimization. We then proceed to prove that the orbit space of such controllers, modulo the coordinate transformation, admits a Riemannian quotient manifold structure. This geometric structure–that is of independent interest–provides an effective approach to derive direct policy optimization algorithms for LQG with a local linear rate convergence guarantee. Subsequently, we show that the proposed approach exhibits significantly faster and more robust numerical performance as compared with ordinary gradient descent.


Bio: Spencer is a PhD candidate at Mehran Mesbahi’s RAIN lab in the Aero and Astro department. Spencer’s main research interests are policy optimization, reinforcement learning, and optimal control. His thesis topic will be on controller synthesis through Riemannian optimization. Here, Riemannian optimization is a toolkit from optimization theory used when your search space is constrained in a smooth non-degenerate way.

See you all Friday!