2017/03/27 by Marc Abeille, Abeille, Marc, Alessandro Lazaric +1 · 30 citations
Computer Science · Decision Sciences · Engineering · Mathematics · #Adaptive Dynamic Programming Control #Advanced Bandit Algorithms Research #Artificial intelligence #Bayesian inference #Bayesian probability #Computer science #Control (management) #Engineering #FOS: Computer and information sciences #Frequentist inference #Function (biology) #Machine Learning (stat.ML) #Mathematical optimization #Mathematics #Quadratic equation #Range (aeronautics) #Regret #Sampling (signal processing) #Smart Grid Energy Management #Statistics #Thompson sampling #stat.ML
paper · pdf · doi:10.48550/arxiv.1703.08972
published in arXiv (Cornell University) (Cornell University)
arxiv created 2017/03/27 · openalex publication_date 2017/03/27 · arxiv updated 2017/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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(T2/3), which is significantly worse than the regret O(√(T)) achieved by the optimism-in-face-of-uncertainty algorithm in LQ control problems.