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.
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.
arXiv:2606. 17319v1 Announce Type: cross Abstract: Motivated by the optimization of bounded binary black-box functions, we study the problem of learning polynomial surrogates over the Boolean hypercube.
arXiv:2606. 15219v1 Announce Type: new Abstract: In this work, we tackle the following question: Can neural networks trained with gradient-based methods achieve the optimal computational-statistical tradeoff in learning Gaussian single-index models?
arXiv:2607. 18559v1 Announce Type: cross Abstract: Gaussian graphical model selection is usually studied under independent sampling, but in many applications the data arise as a single trajectory of a dependent stochastic process.
arXiv:2607. 28856v1 Announce Type: new Abstract: Swap-agnostic learning strengthens classical agnostic learning by allowing the comparator to select a different hypothesis on each level set of the learner's predictions.
arXiv:2608. 10869v1 Announce Type: new Abstract: Worst-case multiclass bounds do not become smaller when the best classifier is already nearly correct: what is missing is an optimistic rate, a guarantee whose fluctuation scales with the oracle risk itself.
arXiv:2606. 11968v1 Announce Type: new Abstract: This paper studies efficient online algorithms for multinomial logistic bandits (MLogB), where the feedback distribution over $K+1$ outcomes follows a multinomial logistic model of $d$-dimensional action vectors.
arXiv:2605. 21107v2 Announce Type: replace Abstract: We study constrained online convex optimization with adversarial time-varying constraints.
arXiv:2505. 21460v2 Announce Type: replace Abstract: We study online calibration of multi-dimensional forecasts over an arbitrary convex set $P \subset \mathbb{R}^d$ relative to an arbitrary norm $|\cdot|$.
arXiv:2602. 05657v2 Announce Type: replace Abstract: The study of tail behaviour of SGD-induced processes has been attracting a lot of interest, due to offering strong guarantees with respect to individual runs of an algorithm.
arXiv:2512. 24152v2 Announce Type: replace-cross Abstract: Sampling based on score diffusions has led to striking empirical results, and has attracted considerable attention from various research communities.
arXiv:2506. 21306v2 Announce Type: replace-cross Abstract: Functions that grow without bound on one side of the real line and decay to zero on the other cannot be approximated uniformly by ordinary polynomials on unbounded domains.