Thompson Sampling for Linear-Quadratic Control Problems - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2017

Thompson Sampling for Linear-Quadratic Control Problems


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.
Fichier principal
Vignette du fichier
main.pdf (745.17 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01493564 , version 1 (21-03-2017)


  • HAL Id : hal-01493564 , version 1


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⟩
296 View
232 Download


Gmail Facebook X LinkedIn More