Abstention budget α in Bayesian BAI induces phase transition to exponential undetected error decay exp(-α²T/8κ_ν²) for Gaussians, with matching bounds and PGWS algorithm achieving it; frequentist setting shows no such gain.
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Bayesian Best-Arm Identification with Abstention: A Polynomial-to-Exponential Phase Transition
Abstention budget α in Bayesian BAI induces phase transition to exponential undetected error decay exp(-α²T/8κ_ν²) for Gaussians, with matching bounds and PGWS algorithm achieving it; frequentist setting shows no such gain.