Fixed Confidence Best Arm Identification in the Bayesian Setting

• DOI: 10.48550/arxiv.2402.10429
• Publication Date: 2024-01-01
• Authors: Jang, Kyoungseok; Komiyama, Junpei; Yamazaki, Kazutoshi
• Keywords: FOS: Computer and information sciences; Computer Science - Machine Learning; Statistics - Machine Learning; Machine Learning (stat.ML); Machine Learning (cs.LG)

We consider the fixed-confidence best arm identification (FC-BAI) problem in the Bayesian setting. This problem aims to find the arm of the largest mean with a fixed confidence level when the bandit model has been sampled from the known prior. Most studies on the FC-BAI problem have been conducted in the frequentist setting, where the bandit model is predetermined before the game starts. We show that the traditional FC-BAI algorithms studied in the frequentist setting, such as track-and-stop and top-two algorithms, result in arbitrarily suboptimal performances in the Bayesian setting. We also obtain a lower bound of the expected number of samples in the Bayesian setting and introduce a variant of successive elimination that has a matching performance with the lower bound up to a logarithmic factor. Simulations verify the theoretical results.