Sharp Root Anti-Concentration for Online Algorithm Configuration

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...

The Cost of Adaptivity: Matching Lower Bounds Across Learning Problems

A finite-horizon composition law for Gaussian certification from M independent coordinates, a familywise certifier protecting every coordinate and time up to T pays optimal normalized squared half-width of order log(eM) + log log(e^eT), within the sample-mean-centered rectangular class.

When Is the Sharp Covariance Envelope Tight? Feature-Only Geometry for Volume-Sampled Least Squares

Prior analyses by Derezinski and Warmuth established all-size sampling identities, selected-OLS unbiasedness, and inverse moments for ordinary volume sampling, while their exact arbitrary-fixed-response loss and prediction-covariance formulas are at the rank-size endpoint s=d. We establish a Loewner envelope for center...

Anytime Last Iterates in Fixed Dimension

Local large deviations for linear-region growth in random piecewise-linear networks

This work introduces a finite-state defect process that records branches whose future splitting can be guaranteed, and uses bridge words to obtain constructive upper-tail lower bounds, and proves the existence of a submultiplicative pressure for N_n, yielding exponential upper bounds for both tails of N_n.

Near-Optimal Dynamic Data Structures for Maximum Depth and Klee's Measure of Boxes

This approach integrates a classic grid-based partition framework with a novel charging analysis that controls the cost of structure-sensitive offline routines within each cell, to perform a global aggregation of the update time, by circumventing the worst-case costs associated with individual cell updates.