Work

Sharp High-Probability Statistical Rates for Heavy-Tailed Nonsmooth Convex Optimization

Year: 2026

Type: preprint

Abstract: We establish sharp high-probability statistical rates for nonsmooth stochastic convex optimization under heavy-tailed noise, closing the confidence-dependence gap in both general convex and strongly convex settings. We consider composite objectives with a Lipschitz convex loss and a known proximal regularizer, accessed through fresh unbiased stochastic subgradients. The centered noise has conditional norm and directional $p$th moments bounded by $L^p$ and $s^p$, respectively, where $1

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.00260

Authors: Zhang, Haihan, Wu, Wendao, Zhang, Chenheng, Li, Yanyi, Zheng, Chunyuan, Fang, Cong, Li, Haoxuan, Lin, Zhouchen

Institution: Peking University

Language: English

Topic: Stochastic Gradient Optimization Techniques

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7215869450

Cites: 9

Cited by: 1

Related to: 10