Learning Controllers for Unstable Linear Quadratic Regulators from a Single Trajectory
Treven, Lenart and Curi, Sebastian and Mutny, Mojmir and Krause, Andreas, Learning Controllers for Unstable Linear Quadratic Regulators from a Single Trajectory.”, 2021. In proceedings of Learning for Dynamics \& Control Conference
Abstract: We present the first approach for learning–from a single trajectory–a linear quadratic regulator (LQR), even for unstable systems, without knowledge of the system dynamics and without requiring an initial stabilizing controller. Our central contribution is an efficient algorithm–\emph {eXploration}–that quickly identifies a stabilizing controller. Our approach utilizes robust System Level Synthesis (SLS), and we prove that it succeeds in a constant number of iterations. Our approach can be used to initialize existing algorithms that require a stabilizing controller as input. When used in this way, it yields a method for learning LQRs from a single trajectory and even for unstable systems, while suffering at most regret.