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Regret Minimization in Partially Observable Linear Quadratic Control (2002.00082v2)

Published 31 Jan 2020 in cs.LG, math.OC, and stat.ML

Abstract: We study the problem of regret minimization in partially observable linear quadratic control systems when the model dynamics are unknown a priori. We propose ExpCommit, an explore-then-commit algorithm that learns the model Markov parameters and then follows the principle of optimism in the face of uncertainty to design a controller. We propose a novel way to decompose the regret and provide an end-to-end sublinear regret upper bound for partially observable linear quadratic control. Finally, we provide stability guarantees and establish a regret upper bound of $\tilde{\mathcal{O}}(T{2/3})$ for ExpCommit, where $T$ is the time horizon of the problem.

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