When and why randomised exploration works (in linear bandits)

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.

Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2502.08870 [cs.LG]

(or arXiv:2502.08870v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2502.08870 Focus to learn more arXiv-issued DOI via DataCite

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