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Why It Matters
We prove the gap-entropy conjecture for fixed-confidence best-arm identification with independent unit-variance Gaussian arms, means in $[0,1]$, and a unique optimal arm.
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Original description
We prove the gap-entropy conjecture for fixed-confidence best-arm identification with independent unit-variance Gaussian arms, means in $[0,1]$, and a unique optimal arm. For each suboptimal arm $i$, let $Δ_i=μ_*-μ_i$ be its gap from the optimal mean, and write $H=\sum_{i\ne *}Δ_i^{-2}$. Let $p_r$ be the fraction of $H$ contributed by arms with $2^{-(r+1)} 0} p_r\log(1/p_r)$. Among all algorithms that identify the optimal arm with probability at least $1-δ$ on every Gaussian instance, the optimal expected number of samples on a given instance, averaged over all permutations of the arm labels,...
Discovered via ArXiv
Research papers and preprints from arXiv.
Publisher: arxiv.org
ID: http://arxiv.org/abs/2609.10529v1 · Indexed about 2 hours ago