Nearly Optimal Fixed-Confidence Best-Arm Identification with 1-Bit Feedback
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arXiv:2608. 02538v1 Announce Type: cross Abstract: This paper is concerned with one-bit mean estimation, where each independent sample is represented by a single binary message.
arXiv:2610. 10488v1 Announce Type: cross Abstract: We study the best arm identification problem in a stochastic environment with a novel form of adversarial perturbations, which we coin Shifting Means.
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.
arXiv:2609. 08564v1 Announce Type: cross Abstract: We study distributed one-dimensional mean estimation under a 1-bit communication constraint.
arXiv:2607. 11635v1 Announce Type: new Abstract: In fixed-budget best-arm identification, also known as ranking and selection, an algorithm has a sampling budget to distribute across $K$ arms.
arXiv:2607. 02896v1 Announce Type: cross Abstract: We ask whether interaction is necessary for order-optimal 1-bit mean estimation over nonparametric finite-moment classes.