@inproceedings{
jang2024fixed,
title={Fixed Confidence Best Arm Identification in the Bayesian Setting},
author={Kyoungseok Jang and Junpei Komiyama and Kazutoshi Yamazaki},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=hFTye9Ge40}
}
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.
Fixed Confidence Best Arm Identification in the Bayesian Setting
Kyoungseok Jang Junpei Komiyama Kazutoshi Yamazaki