Focus Period Lund 2026
PhD Student
King Abdullah University of Science and Technology – KAUST (Saudi Arabia)
Hanmin Li is a PhD candidate in Computer Science at King Abdullah University of Science and Technology (KAUST), supervised by Prof. Peter Richtárik. His research centers on optimization and large language models (LLMs), with an emphasis on improving training efficiency, scalability, and distributed learning. His work spans first-order methods, convex and non-convex optimization. Prior to his PhD, he earned an M.S. in Computer Science at KAUST and a B.S. in Computer Science and Technology from the School of the Gifted Young at the University of Science and Technology of China (USTC).
Presenting: Stabilizing Proximal Updates: Trust Regions, Linear Descent, and Connections to Modern ML Optimizers
Proximal methods play a central role in modern machine learning, appearing implicitly in optimizers such as AdamW, in gradient clipping and projection steps, and in local training procedures like FedProx. Despite their robustness and stability, the classical Proximal Point Method (PPM) admits only sublinear convergence under general convexity unless a stronger condition such as strong convexity, is assumed. In this talk, we introduce a trust-region stabilized proximal framework that achieves linear descent without requiring smoothness or strong convexity. The key idea is simple: restrict each proximal update to a local neighborhood of the currentiterate. We show that this stabilization enforces a uniform lower bound on the proximal displacement away from the solution set, which becomes the fundamental driver of linear decrease in function values outside any prescribedneighborhood.
Our analysis reveals two complementary stabilization mechanisms: tuning the regularization parameter while fixing the trust-region radius, or fixing the regularization and selecting the radius via a uniform displacement bound. Under strong convexity, the trust-region constraint becomes redundant, recovering classical linear convergence guarantees. The results provide a unified view of proximal regularization and trust-region control, bridging classical convex optimization theorywith stabilization techniques widely used in modern machine learning.