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A Sharp Dynamic Haussler Lemma

Shihao Shao, Dacheng Tao · 2026 · arXiv

DOI: 10.48550/arXiv.2610.29898 · open-access PDF

Korean

Haussler's covering lemma (JCTA 1995)는 표준화된 $\ell_p$의 bounded real-value classes에 대한 뚜렷한 글로벌 동적을 증명합니다. <d=operatorname{sfat}_{\varepsilon/32}(\mathcal F)$>를 쓰면 모든 지평선과 $0&lt\varepsilon&lt;1/2$에 대한 최대 $(C/varepsilon^p)$d의 크기의 글로벌 동적 커버를 얻습니다.

Machine translation (Meta M2M100); the English original follows.

Abstract

Haussler's covering lemma (JCTA 1995) gives the sharp $(C/δ)^d$ metric-entropy bound for binary VC classes under normalized $\ell_1$ distance. We prove a sharp global dynamic analogue for bounded real-valued classes in normalized $\ell_p$, for every $1\le p&lt;\infty$. Writing $d=\operatorname{sfat}_{\varepsilon/32}(\mathcal F)$, we obtain a global dynamic cover of size at most $(C/\varepsilon^p)^d$ for every horizon and $0&lt;\varepsilon&lt;1/2$. Here a single family of deterministic causal experts, fixed independently of the instance sequence, covers every target on every sequence. For $0&lt

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