When and why randomised exploration works (in linear bandits)

Published: 18 Dec 2024, Last Modified: 14 Feb 2025ALT 2025EveryoneRevisionsBibTeXCC BY 4.0
Abstract:

We provide an approach for the analysis of randomised exploration algorithms like Thompson sampling that does not rely on forced optimism or posterior inflation. With this, we demonstrate that in the $d$-dimensional linear bandit setting, when the action space is smooth and strongly convex, randomised exploration algorithms enjoy an $n$-step regret bound of the order $O(d\sqrt{n} \log(n))$. Notably, this shows for the first time that there exist non-trivial linear bandit settings where Thompson sampling can achieve optimal dimension dependence in the regret.

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Submission Number: 140
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