From Optimality to Robustness: Dirichlet Sampling Strategies in Stochastic Bandits
This addresses robustness issues for practitioners in decision-making problems like agriculture, where precise distribution knowledge may be lacking, though it is incremental as it builds on existing bandit frameworks.
The paper tackles the problem of robustness in stochastic multi-arm bandits to model misspecification, showing that a Dirichlet Sampling algorithm achieves optimal regret for bounded distributions and logarithmic regret for semi-bounded ones, with a simple tuning providing robustness for unbounded distributions at a slightly worse than logarithmic cost.
The stochastic multi-arm bandit problem has been extensively studied under standard assumptions on the arm's distribution (e.g bounded with known support, exponential family, etc). These assumptions are suitable for many real-world problems but sometimes they require knowledge (on tails for instance) that may not be precisely accessible to the practitioner, raising the question of the robustness of bandit algorithms to model misspecification. In this paper we study a generic Dirichlet Sampling (DS) algorithm, based on pairwise comparisons of empirical indices computed with re-sampling of the arms' observations and a data-dependent exploration bonus. We show that different variants of this strategy achieve provably optimal regret guarantees when the distributions are bounded and logarithmic regret for semi-bounded distributions with a mild quantile condition. We also show that a simple tuning achieve robustness with respect to a large class of unbounded distributions, at the cost of slightly worse than logarithmic asymptotic regret. We finally provide numerical experiments showing the merits of DS in a decision-making problem on synthetic agriculture data.