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Gap-Entropy Conjecture Positively Resolved for Gaussian Arms

By PulseAugur Editorial · [2 sources] ·

Researchers have positively resolved the gap-entropy conjecture for fixed-confidence best-arm identification problems involving independent unit-variance Gaussian arms. The study establishes bounds on the optimal expected number of samples required, which are related to the gap between suboptimal arms and the optimal arm, as well as an entropy term derived from the distribution of these gaps. An algorithm is presented that achieves this bound, plus an additional term related to the smallest gap to a competitor. AI

IMPACT This theoretical advancement in multi-armed bandit problems could inform more efficient AI training and reinforcement learning algorithms.

RANK_REASON Academic paper published on arXiv with associated code/tools.

Read on Hugging Face Daily Papers →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

Gap-Entropy Conjecture Positively Resolved for Gaussian Arms

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COVERAGE [2]

  1. Hugging Face Daily Papers TIER_1 English(EN) ·

    A positive resolution of the gap-entropy conjecture

    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_…

  2. arXiv stat.ML TIER_1 English(EN) · P. M. Aronow, Nathan Kallus, Patrick Lopatto ·

    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 a unique optimal arm. For each suboptimal arm $i$, let $\Delta_i=\mu_*-\mu_i$ be …

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