Thompson Sampling for LinearQuadratic Control Problems
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Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:12461254, 2017.
Abstract
We consider the explorationexploitation tradeoff in linear quadratic (LQ) control problems, where the state dynamics is linear and the cost function is quadratic in states and controls. We analyze the regret of Thompson sampling (TS) (a.k.a. posteriorsampling for reinforcement learning) in the frequentist setting, i.e., when the parameters characterizing the LQ dynamics are fixed. Despite the empirical and theoretical success in a wide range of problems from multiarmed bandit to linear bandit, we show that when studying the frequentist regret TS in control problems, we need to tradeoff the frequency of sampling optimistic parameters and the frequency of switches in the control policy. This results in an overall regret of $O(T^2/3)$, which is significantly worse than the regret $O(\sqrtT)$ achieved by the optimisminfaceofuncertainty algorithm in LQ control problems.
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