广州数学大讲坛第五期

第四十八讲——瑞典林雪平大学何川助理教授学术报告

题目：Complexity of normalized stochastic first-order methods with momentum under heavy-tailed noise

时间：2025年7月11日（星期五）上午10:20-11:30

地点：理学实验楼312

报告人：何川 助理教授

摘要：In this work, we propose practical normalized stochastic first-order methods with Polyak momentum, multi-extrapolated momentum, and recursive momentum for solving unconstrained optimization problems. These methods employ dynamically updated algorithmic parameters and do not require explicit knowledge of problem-dependent quantities such as the Lipschitz constant or noise bound. We establish first-order oracle complexity results for finding approximate stochastic stationary points under heavy-tailed noise and weakly average smoothness conditions—both of which are weaker than the commonly used bounded variance and mean-squared smoothness assumptions. Our complexity bounds either improve upon or match the best-known results in the literature. Numerical experiments are presented to demonstrate the practical effectiveness of the proposed methods.

The paper is available on arXiv at //arxiv.org/pdf/2506.11214

报告人简介：

何川，博士，瑞典林雪平大学数学系助理教授，在SIOPT, MOR, JMLR, TMLR, IJOC, COAP等杂志发表多篇论文。