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The stochastic multi-arm bandit problem has been extensively studied understandard assumptions on the arm's distribution (e.g bounded with known support,exponential family, etc). These assumptions are suitable for many real-worldproblems but sometimes they require knowledge (on tails for instance) that maynot be precisely accessible to the practitioner, raising the question of therobustness of bandit algorithms to model misspecification. In this paper westudy a generic Dirichlet Sampling (DS) algorithm, based on pairwisecomparisons of empirical indices computed with re-sampling of the arms'observations and a data-dependent exploration bonus. We show that differentvariants of this strategy achieve provably optimal regret guarantees when thedistributions are bounded and logarithmic regret for semi-bounded distributionswith a mild quantile condition. We also show that a simple tuning achieverobustness with respect to a large class of unbounded distributions, at thecost of slightly worse than logarithmic asymptotic regret. We finally providenumerical experiments showing the merits of DS in a decision-making problem onsynthetic agriculture data.

From Optimality to Robustness: Dirichlet Sampling Strategies in Stochastic Bandits