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. For cube-supported coefficients, this speed is equivalent, up to universal constants, to the projective Lipschitz constant. This yields a sharp, dimension-free characterization and removes the previous $\sqrt N$ loss. For monic degree-$d$ polynomials ...
| Authors | Zijun Wang, Yuchen Miao, Yifan Hu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 3 August 2026 |
| Last updated at source | 3 August 2026 |
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