Academic Report of the School of Mathematical Sciences No. 061

(Series Report on High-Level University Construction No. 1083)

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

Speaker: Dr. Chuan He (Assistant Professor, Linköping University, Sweden)

Date & Time: July 9, 2025, 10:00–11:30 AM

Venue: Huixing Building, Room 514

Abstract: 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.

Biography: Dr. Chuan He is an Assistant Professor at the Department of Mathematics, Linköping University, Sweden. He has published multiple papers in journals including SIOPT, MOR, JMLR, TMLR, IJOC, and COAP.

All faculty and students are welcome!

Invited by: Kai Tu

School of Mathematical Sciences

June 27, 2025