Bayesian Best-Arm Identification with Abstention: A Polynomial-to-Exponential Phase Transition
We study the Bayesian fixed-budget best-arm identification problem in which a learner can abstain from making a terminal recommendation. Subject to an abstention budget $α$, we analyze the probability of undetected error--the risk of recommending a suboptimal arm without abstaining. Our central finding is that abstention induces a phase transition: without abstention, the error probability decays polynomially in the sampling budget $T$; in contrast, introducing any small positive abstention budget shifts this to an exponential decay. For Gaussian priors and rewards, in the regime $T\to\infty$ followed by $α\downarrow0$, we establish exact matching information-theoretic lower bounds and al...
| Authors | Yuqi Huang, Yunlong Hou, Vincent Y. F. Tan |
|---|---|
| Primary category | cs.LG |
| Published | 28 June 2026 |
| Last updated at source | 28 June 2026 |
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