Thesis of Marc Abeille

Exploration-Exploitation with Thompson Sampling in Linear Systems

This dissertation is dedicated to the study of the Thompson Sampling (TS) algorithms designed to address the exploration-exploitation dilemma that is inherent in sequential decision-making under uncertainty. As opposed to algorithms derived from the optimism-in-the-face-of-uncertainty (OFU) principle, where the exploration is performed by selecting the most favorable model within the set of plausible one, TS algorithms rely on randomization to enhance the exploration, and thus are much more computationally e cient. We focus on linearly parametrized problems that allow for continuous state-action spaces, namely the Linear Bandit (LB) problems and the Linear Quadratic (LQ) control problems. We derive two novel analyses for the regret of TS algorithms in those settings. While the obtained regret bound for LB is similar to previous results, the proof sheds new light on the functioning of TS, and allows us to extend the analysis to LQ problems. As a result, we prove the first regret bound for TS in LQ, and show that the frequentist regret is of order O(sqrt(T)) which matches the existing guarantee for the regret of OFU algorithms in LQ. Finally, we propose an application of exploration-exploitation techniques to the practical problem of portfolio construction, and discuss the need for active exploration in this setting.

Jury

Thesis of the SequeL team defended on 13 December 2017

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