Bayesian Fixed-Confidence Best-Arm Identification with Abstention

The paper investigates Bayesian fixed‑confidence best‑arm identification where a learner may abstain from a final recommendation. It introduces the Screen‑and‑Confirm (S&C) algorithm, analyzes its expected stopping time, and derives lower bounds for any algorithm under error probability δ and abstention budget α constraints. For Gaussian priors, the authors provide matching upper and lower bounds, characterize exact constants for practical regimes, and show that S&C achieves optimal α–dependent rates, improving on previous results when abstention is disallowed.

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