The paper introduces a new simultaneous pointwise majorization framework for Banach‑valued stochastic processes that possess finite‑metric mixed‑tail increments. By assuming an anchored process satisfies a tail bound involving multiple pseudo‑metrics and orders, the authors derive a high‑probability envelope that holds uniformly over the index set, with terms expressed through integrals of log‑covering numbers and distance functions. This result generalizes single‑metric sub‑Weibull bounds and, in the Gaussian case, improves existing pointwise upper bounds by removing extraneous logarithmic factors.
By Haichen Hu, David Simchi-Levi
arXiv:2608. 13467v1 Announce Type: new Abstract: We study the Moreau--Yosida unadjusted Langevin algorithm (MYULA) for the nonsmooth composite target \[ \pi(dx)\propto \exp\{-f(x)-g(x)\}\,dx, \qquad x\in\mathbb R^d, \] where \(f\) is \(m\)-strongly convex with \(L_f\)-Lipschitz gradient and \(g\) is convex and \(G\)-Lipschitz.
By Yuchen Xin, Zhihua Zhang
arXiv:2607. 16384v1 Announce Type: new Abstract: For stochastic gradient descent (SGD) with a constant stepsize $\alpha$, the invariant law of the iterates, centered at a minimizer, describes the behavior of the algorithm over long time horizons.
By Jingyi Zhang, Cheng Mao, Debankur Mukherjee
arXiv:2608. 09870v1 Announce Type: cross Abstract: Uniform stability is a classical tool for controlling the generalization error of a learning algorithm.
By Thanh Nguyen-Cung, Binh T. Nguyen
arXiv:2610.27022v1 Announce Type: cross
Abstract: We study Gaussian kernel approximation and regularized logistic classification on a connected compact smooth embedded manifold $X\subset\mathbb R^d$...
By Guanhang Lei, Lei Shi, Xiaoming Yuan
arXiv:2605. 12461v2 Announce Type: replace-cross Abstract: We propose an algorithm to sample from composite log-concave distributions over $\mathbb{R}^d$, i.
By Linghai Liu, Sinho Chewi
arXiv:2609. 12594v1 Announce Type: new Abstract: We study the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA) for $\pi(\,\mathrm{d} x)\propto e^{-f(x)-g(x)}\,\mathrm{d} x$, where $f\in C^2(\mathbb{R}^d)$ is $m$-strongly convex with $L_f$-Lipschitz gradient and $g:\mathbb{R}^d\to\mathbb{R}$ is convex and globally $G$-Lipschitz.
By Yuchen Xin, Zhihua Zhang
arXiv:2609.15170v1 Announce Type: new
Abstract: We study stochastic linear contextual bandits with arbitrary action menus that may depend on the fixed parameter and the interaction history. We establ...
By Tianyuan Jin
arXiv:2609.09480v1 Announce Type: cross
Abstract: We develop Gaussian approximation bounds in higher-order Wasserstein distance $W_p$, $p\geq2$, for sums of multivariate martingale differences genera...
By Yixuan Zhang, Qiaomin Xie
arXiv:2609. 11837v1 Announce Type: cross Abstract: We study the nonlocal continuity equation \[ \partial_t\mu_b =\operatorname{div}\!
By Andrea Agazzi, Giuseppe Bruno, Federico Pasqualotto, Philippe Rigollet
arXiv:2409. 08469v4 Announce Type: replace-cross Abstract: We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy ($\mathsf{KSD}$) and Wasserstein-2 metrics.
By Sayan Banerjee, Krishnakumar Balasubramanian, Promit Ghosal
arXiv:2606. 06384v2 Announce Type: replace-cross Abstract: The sub-Gaussian parameter (also called the variance proxy) of a mean-zero random variable $X$ is defined as $\xi^2_\star = \sup_{\lambda \in \mathbb{R}} L(\lambda)$ where $L(\lambda) = \frac{2}{\lambda^2} \log \mathbb{E} e^{\lambda X}$ is a weighted cumulant generating function.
By Jason Liu, Min Xu, Jinchuan Xing