English

Stochastic Weakly Convex Optimization Beyond Lipschitz Continuity

Optimization and Control 2024-11-07 v2 Machine Learning

Abstract

This paper considers stochastic weakly convex optimization without the standard Lipschitz continuity assumption. Based on new adaptive regularization (stepsize) strategies, we show that a wide class of stochastic algorithms, including the stochastic subgradient method, preserve the O(1/K)\mathcal{O} ( 1 / \sqrt{K}) convergence rate with constant failure rate. Our analyses rest on rather weak assumptions: the Lipschitz parameter can be either bounded by a general growth function of x\|x\| or locally estimated through independent random samples.

Keywords

Cite

@article{arxiv.2401.13971,
  title  = {Stochastic Weakly Convex Optimization Beyond Lipschitz Continuity},
  author = {Wenzhi Gao and Qi Deng},
  journal= {arXiv preprint arXiv:2401.13971},
  year   = {2024}
}
R2 v1 2026-06-28T14:26:43.280Z