Title: Finite Sample Guarantees for Control of an Unknown Linear
Dynamical System

Speaker: Stephen Tu, UC Berkeley

Abstract: In principle, control of a physical system is accomplished by first
deriving a faithful model of the underlying dynamics from first principles, and
then solving an optimal control problem with the modeled dynamics. In
practice, the system may be too complex to precisely characterize, and an
appealing alternative is to instead collect trajectories of the system and fit
a model of the dynamics from the data. How many samples are needed for this to
work? How sub-optimal is the resulting controller?

In this talk, I will shed light on these questions when the underlying
dynamical system is linear and the control objective is quadratic, a classic
optimal control problem known as the Linear Quadratic Regulator. Despite
the simplicity of linear dynamical systems, deriving finite-time guarantees for
both system identification and controller performance is non-trivial. I will
first talk about our results in the "one-shot" setting, where
measurements are collected offline, a model is estimated from the data, and a
controller is synthesized using the estimated model with confidence bounds.
Then, I will discuss our recent work on guarantees in the online regret
setting, where noise injected into the system for learning the dynamics needs
to trade-off with state regulation.

This talk is based on joint work with Sarah Dean, Horia
Mania, Nikolai Matni, and Benjamin Recht.

Bio: Stephen Tu is a Ph.D. candidate in the
Electrical Engineering and Computer Sciences department at the University of
California, Berkeley. His research interests are in machine learning,
optimization, and control theory.