arXiv Machine Learning By Zijun Wang, Yuchen Miao, Yifan Hu, Huanmin Liu

Sharp Root Anti-Concentration via Projective Incidence and Ordered Root Laws

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arXiv:2608. 01670v1 Announce Type: new Abstract: This paper answers the one-dimensional local root anti-concentration questions posed by Balcan, Pegden, and Sharma in the context of online optimization of piecewise-Lipschitz functions.

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Sharp Root Anti-Concentration via Projective Incidence and Ordered Root Laws

This paper answers the one-dimensional local root anti-concentration questions posed by Balcan, Pegden, and Sharma in the context of online optimization of piecewise-Lipschitz functions. For a homogeneous feature curve and coefficients whose density relative to the uniform law on a symmetric convex body $K$ is bounded by $A$, we show that the worst-case interval-hitting constant equals $A$ times a section-averaged projective incidence speed.