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Fri Jul 13 02:00 AM -- 02:20 AM (PDT) @ A5
Online Linear Quadratic Control
Alon Cohen · Avinatan Hasidim · Tomer Koren · Nevena Lazic · Yishay Mansour · Kunal Talwar
We study the problem of controlling linear time-invariant systems with known noisy dynamics and adversarially chosen quadratic losses. We present the first efficient online learning algorithms in this setting that guarantee $O(\sqrt{T})$ regret under mild assumptions, where $T$ is the time horizon. Our algorithms rely on a novel SDP relaxation for the steady-state distribution of the system. Crucially, and in contrast to previously proposed relaxations, the feasible solutions of our SDP all correspond to ``strongly stable'' policies that mix exponentially fast to a steady state.