# Thompson Sampling for Linear-Quadratic Control Problems

2 SEQUEL - Sequential Learning
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : We consider the exploration-exploitation 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. posterior-sampling 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 multi-armed bandit to linear bandit, we show that when studying the frequentist regret \ts in control problems, we need to trade-off 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 $O(\sqrt{T})$ achieved by the optimism-in-face-of-uncertainty algorithm in LQ control problems.
Document type :
Conference papers

https://hal.inria.fr/hal-01493564
Contributor : Alessandro Lazaric <>
Submitted on : Tuesday, March 21, 2017 - 5:39:46 PM
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• HAL Id : hal-01493564, version 1

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Marc Abeille, Alessandro Lazaric. Thompson Sampling for Linear-Quadratic Control Problems. AISTATS 2017 - 20th International Conference on Artificial Intelligence and Statistics, Apr 2017, Fort Lauderdale, United States. ⟨hal-01493564⟩

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