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This paper studies the fixed-confidence best arm identification (BAI) problemin the bandit framework in the canonical single-parameter exponential models.For this problem, many policies have been proposed, but most of them requiresolving an optimization problem at every round and/or are forced to explore anarm at least a certain number of times except those restricted to the Gaussianmodel. To address these limitations, we propose a novel policy that combinesThompson sampling with a computationally efficient approach known as the bestchallenger rule. While Thompson sampling was originally considered formaximizing the cumulative reward, we demonstrate that it can be used tonaturally explore arms in BAI without forcing it. We show that our policy isasymptotically optimal for any two-armed bandit problems and achieves nearoptimality for general $K$-armed bandit problems for $K\geq 3$. Nevertheless,in numerical experiments, our policy shows competitive performance compared toasymptotically optimal policies in terms of sample complexity while requiringless computation cost. In addition, we highlight the advantages of our policyby comparing it to the concept of $\beta$-optimality, a relaxed notion ofasymptotic optimality commonly considered in the analysis of a class ofpolicies including the proposed one.

Thompson Exploration with Best Challenger Rule in Best Arm Identification