Learning Linear-Quadratic Regulators Efficiently with only $\sqrt{T}$ Regret

TL;DR

This paper introduces a computationally-efficient algorithm for Linear Quadratic Control systems that achieves near-optimal regret bounds, addressing a longstanding open problem in the field.

Contribution

It provides the first efficient algorithm with $ ilde{O}( oot T)$ regret for unknown linear quadratic control, resolving key open questions.

Findings

Achieves $ ilde{O}( oot T)$ regret in linear quadratic control

First computationally-efficient algorithm with this regret bound

Resolves open problems from prior foundational works

Abstract

We present the first computationally-efficient algorithm with $\widetilde O(\sqrt{T})$ regret for learning in Linear Quadratic Control systems with unknown dynamics. By that, we resolve an open question of Abbasi-Yadkori and Szepesv\'ari (2011) and Dean, Mania, Matni, Recht, and Tu (2018).