arXiv:2609. 20687v1 Announce Type: cross Abstract: We study first-order black-box convex optimization over an $\ell_p$-ball for objectives Lipschitz in the $\ell_q$-norm, solving in the affirmative the nonsmooth version of the COLT open question (Guz15b) on whether the geometry of a smaller feasible set ($p < q$) can improve convergence rates in convex optimization, and matching prior lower bounds up to logarithmic factors.
By David Mart\'inez-Rubio, Brian Bullins, Crist\'obal Guzm\'an, Mathieu Molina
arXiv:2602. 16568v2 Announce Type: replace-cross Abstract: Sparse recovery is among the most well-studied problems in learning theory and high-dimensional statistics.
By Ziyun Chen, Jerry Li, Kevin Tian, Yusong Zhu
We study the problem of \emph{adversarially robust} PAC learning. In this framework, the learner observes independent samples from an unknown distribution over $\mathcal{X} \times \{0,1\}$, as in clas...
arXiv:2605.13684v2 Announce Type: replace
Abstract: We study the optimal scale at which real-valued function classes exhibit uniform convergence and learnability. Our main result establishes a scale-...
By Shashaank Aiyer, Yishay Mansour, Shay Moran, Han Shao, Tom Waknine
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.
By Jasper van Doornmalen, Mathieu Molina, Victor Verdugo, Jos\'e Verschae
arXiv:2004. 05813v3 Announce Type: replace-cross Abstract: Suppose that we are given independent, identically distributed random samples $x_1,\cdots,x_n$ from a mixture at most $k$ many $d$-dimensional spherical Gaussian distributions $\mu_1,\cdots,\mu_{k_0}$ of identical and known variance $\sigma^2$ in each coordinate, such that the minimum $\ell^2$ distance between two distinct centers $y_l$ and $y_j$ is greater than $2\Delta\sigma \min\{\sqrt{d},\sqrt k\}$, where $\Delta>C_0$, and $C_0$ is a sufficiently large universal constant.
By Somnath Chakraborty, Hariharan Narayanan
arXiv:2609.24260v1 Announce Type: cross
Abstract: We study the problem of \emph{adversarially robust} PAC learning. In this framework, the learner observes independent samples from an unknown distrib...
By Steve Hanneke, Amirreza Shaeiri
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.
By M. J. Wainwright
arXiv:2609. 29696v1 Announce Type: new Abstract: We construct, for every function class $\mathcal{F}\subseteq[0,1]^{\mathcal{X}}$ and every accuracy $0<\alpha\le 1$, an agnostic sample compression scheme for the empirical squared loss: for every finite sample $S\in(\mathcal{X}\times[0,1])^m$ with arbitrary (noisy) labels, the scheme stores at most $O(\mathrm{fat}(\mathcal{F},c'\alpha)\cdot\log^3(2/\alpha))$ original labeled examples and auxiliary bits, independent of the sample size $m$, and reconstructs a function $\hat f$ with $L_2(\hat f,S)\le\inf_{f\in\mathcal{F}}L_2(f,S)+\alpha$.
By Guangjian Zhang
arXiv:2606. 14335v1 Announce Type: cross Abstract: Recovering structural information from noisy high-dimensional data is a fundamental task in statistical inference.
By Zhe Hou, Jingcheng Liu
arXiv:2608. 15472v1 Announce Type: cross Abstract: The problem of networked information aggregation, studied in Kearns et al.
By Ambar Pal
arXiv:2609. 20883v1 Announce Type: new Abstract: Despite the widespread use and success of generative AI techniques today, theoretical guarantees on learning a distribution supported in $d$ dimensions from $n$ samples degrade as $O(n^{-1/\Theta(d)})$, though shown to be minimax optimal.
By Saumya Goyal, Barnab\'as P\'oczos