Year: 2026
Type: preprint
Abstract: We study optimizing $L$-smooth and $μ$-Polyak-Lojasiewicz (PL) objectives with unbiased stochastic gradients under $α$-heavy-tailed noise ($1<α\le 2$). In the unrestricted high-dimensional setting, we establish the noise-adaptive lower bound for attaining $ε$-suboptimal function value. Under the generalized mirror-PL condition, we propose a centered-clipped mirror-descent method that achieves a high-probability upper bound matching the lower bound up to logarithmic factors. We further provide the improved tight stochastic complexity in fixed dimensions.
Source: arXiv (Cornell University)
Authors: Ou, Weiming, Wang, Xiao
Institution: Shanghai University of Finance and Economics
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208757937