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arXiv · 1806.07104

Online Linear Quadratic Control

Alon Cohen·Avinatan Hassidim·Tomer Koren·Nevena Lazic·Yishay Mansour·Kunal Talwar
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Abstract

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.

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Alon Cohen, Avinatan Hassidim, Tomer Koren, Nevena Lazic, Yishay Mansour, Kunal Talwar. 2018-06-19. Online Linear Quadratic Control. https://arxiv.org/abs/1806.07104

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