Bounded regret in stochastic multi-armed bandits

Sébastien Bubeck; Vianney Perchet; Philippe Rigollet

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arXiv · 1302.1611

Bounded regret in stochastic multi-armed bandits

Sébastien Bubeck·Vianney Perchet·Philippe Rigollet

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Abstract

We study the stochastic multi-armed bandit problem when one knows the value $μ^{(\star)}$ of an optimal arm, as a well as a positive lower bound on the smallest positive gap $Δ$. We propose a new randomized policy that attains a regret {\em uniformly bounded over time} in this setting. We also prove several lower bounds, which show in particular that bounded regret is not possible if one only knows $Δ$, and bounded regret of order $1/Δ$ is not possible if one only knows $μ^{(\star)}$

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BibTeX RIS

Sébastien Bubeck, Vianney Perchet, Philippe Rigollet. 2013-02-12. Bounded regret in stochastic multi-armed bandits. https://arxiv.org/abs/1302.1611

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