Fighting Bandits with a New Kind of Smoothness

Jacob Abernethy; Chansoo Lee; Ambuj Tewari

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arXiv · 1512.04152

Fighting Bandits with a New Kind of Smoothness

Jacob Abernethy·Chansoo Lee·Ambuj Tewari

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Abstract

We define a novel family of algorithms for the adversarial multi-armed bandit problem, and provide a simple analysis technique based on convex smoothing. We prove two main results. First, we show that regularization via the \emph{Tsallis entropy}, which includes EXP3 as a special case, achieves the $\Theta(\sqrt{TN})$ minimax regret. Second, we show that a wide class of perturbation methods achieve a near-optimal regret as low as $O(\sqrt{TN \log N})$ if the perturbation distribution has a bounded hazard rate. For example, the Gumbel, Weibull, Frechet, Pareto, and Gamma distributions all satisfy this key property.

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BibTeX RIS

Jacob Abernethy, Chansoo Lee, Ambuj Tewari. 2015-12-14. Fighting Bandits with a New Kind of Smoothness. https://arxiv.org/abs/1512.04152

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