Fighting Bandits with a New Kind of Smoothness

12/14/2015

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by   Jacob Abernethy, et al.

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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 Tsallis entropy, which includes EXP3 as a special case, achieves the Θ(√(TN)) minimax regret. Second, we show that a wide class of perturbation methods achieve a near-optimal regret as low as O(√(TN 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.