Fixed Confidence Best Arm Identification in the Bayesian Setting
<|reference_start|>Fixed Confidence Best Arm Identification in the Bayesian Setting: 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.<|reference_end|>
@article{jang2024fixed,
    title={Fixed Confidence Best Arm Identification in the Bayesian Setting},
    author={Kyoungseok Jang, Junpei Komiyama, Kazutoshi Yamazaki},
    journal={arXiv preprint arXiv:2402.10429},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.10429},
    primaryClass={stat.ML cs.LG}
}