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A positive resolution of the gap-entropy conjecture
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arXiv Statistics ML
Sep 10
A positive resolution of the gap-entropy conjecture
arXiv:2609.10529v1 Announce Type: cross Abstract: We prove the gap-entropy conjecture for fixed-confidence best-arm identification with independent unit-variance Gaussian arms, means in $[0,1]$, and...
arXiv AI
Sep 15
Gap Entropy and Almost Instance-Wise Optimal Best-Arm Identification
arXiv:2609.13703v1 Announce Type: cross Abstract: In the best-arm identification problem, we are given $n$ stochastic arms with unknown means and wish to identify the arm with the largest mean with p...
arXiv Machine Learning
Oct 23
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.
arXiv Statistics ML
Oct 26
On the Complexity of Best-Arm Identification in Non-Stationary Linear Bandits
arXiv:2603. 10346v2 Announce Type: replace Abstract: We study the fixed-budget best-arm identification (BAI) problem in non-stationary linear bandits.
arXiv Machine Learning
Jul 21
Tight Sample Bounds for Renyi and Min-Entropy Estimation
arXiv:2607. 16966v1 Announce Type: cross Abstract: Estimating entropy from samples is fundamental in information theory and property testing.
arXiv Machine Learning
Oct 15
Hypothesis Selection via Weighted Medians
arXiv:2610.20375v1 Announce Type: cross Abstract: Given $n$ distributions (hypotheses) $\mathcal H=\{H_1,\ldots,H_n\}$ and samples from an unknown target distribution $P$, proper hypothesis selection...