Academic Report of School of Mathematical Sciences [2026] No. 058

(Series Report for High-Level University Construction No. 1317)

Title：A variance reduced framework for (non)smooth nonconvex–nonconcave stochastic minimax problems with extended Kurdyka–Łojasiewicz property

Speaker：Yangyang Xu, Associate Professor ( Rensselaer Polytechnic Institute)

Time：15:30-16:30, June 16, 2026

Location：Room 304, Alumni Plaza, Yuehai Campus

Abstract: In this talk, I will present an algorithm for solving stochastic constrained minimax optimization problems with nonconvex--nonconcave structure, a central problem in modern machine learning, for which reliable and efficient algorithms remain largely unexplored due to its inherent challenges.  

Prior approaches for nonconvex minimax optimization often require (strong) concavity on the maximization part, or certain restrictive geometric assumptions on the joint objective to have guaranteed convergence. In contrast, our method only assumes weak convexity in the primal variable and the extended Kurdyka–Łojasiewicz (KL) property in the dual variable, significantly broadening the class of tractable problems. To this end, we propose a variance reduced algorithm that provably handles this general setting. To the best of our knowledge, this is the first unified framework that jointly accommodates weak convexity, the extended KL property, and variance-reduced stochastic updates, making it highly suitable for large-scale applications.

Speaker Profile：Yangyang Xu is an Associate Professor in the Department of Mathematical Sciences at Rensselaer Polytechnic Institute. He received his B.S. in Computational Mathematics from Nanjing University in 2007, his M.S. in Operations Research from the Chinese Academy of Sciences in 2010, and his Ph.D. in Computational and Applied Mathematics from Rice University in 2014. His research focuses on optimization theory and algorithms and their applications in machine learning, statistics, and signal processing. His recent work centers on stochastic optimization, robust machine learning, large-scale constrained optimization, and distributed optimization. He currently serves as an Associate Editor for Mathematics of Operations Research.

Faculty and students are welcome to attend!

Invited by: Yuqia Wu

School of Mathematical Sciences

June 15, 2026