Fast and Regret Optimal Best Arm Identification: Fundamental Limits and Low-Complexity Algorithms

This paper considers a stochastic Multi-Armed Bandit (MAB) problem with dual objectives: (i) quick identification and commitment to the optimal arm, and (ii) reward maximization throughout a sequence of T consecutive rounds. Though each objective has been individually well-studied, i.e., best arm identification for (i) and regret minimization for (ii), the simultaneous realization of both objectives remains an open problem, despite its practical importance. This paper introduces Regret Optimal Best Arm Identification (ROBAI) which aims to achieve these dual objectives.