Time：2026.1.16
Tencent meeting: 770-388-557
Organizers:
Zhennan Zhou, Westlake University
Hai Zhu, Westlake University
9:00-9:45
Minxin Zhang, Hedrick Assistant Adjunct Professor, University of California, Los Angeles
Bio: Dr. Minxin Zhang is a Hedrick Assistant Adjunct Professor in the Department of Mathematics at the University of California, Los Angeles, mentored by Prof. Hayden Schaeffer and Prof. Deanna Needell. She received her Ph.D. in Mathematics from the University of California San Diego, where she was advised by Prof. Philip Gill. Her research interests include nonlinear and nonconvex optimization, global optimization, optimization for deep learning and scientific computing, randomized numerical linear algebra, and tensor computation.
Title: Algorithmic Design and Analysis of Nonconvex Optimization for Deep Learning and Scientific Computing
Abstract: Modern machine learning and scientific computing pose optimization challenges of unprecedented scale and complexity, demanding fundamental advances in both theory and algorithmic design for nonconvex optimization. This talk presents two recent advances that address these challenges by exploiting matrix and tensor structures, integrating adaptivity, and leveraging sampling techniques. In the first part, I introduce AdaGO, a new optimizer that combines orthogonalized momentum updates with adaptive learning rates. Building on the recent success of the Muon optimizer in large language model training, AdaGO incorporates an AdaGrad-type step size that scales orthogonalized update directions by accumulated past gradient norms. This design preserves the structural advantage of orthogonalized updates while adapting step sizes to noise and the optimization landscape. We establish optimal convergence rates for smooth nonconvex functions and demonstrate improved empirical performance over Muon and Adam across varied tasks. The second part focuses on zeroth-order global optimization. We develop a theoretical framework for inexact proximal point (IPP) methods for global optimization, establishing convergence guarantees when proximal operators are estimated either deterministically or stochastically. The quadratic regularization in the proximal operator induces a concentrated Gibbs measure landscape that facilitates effective sampling. We propose two sampling-based practical algorithms: TT-IPP, which constructs a low-rank tensor-train (TT) approximation using a randomized TT-cross algorithm, and MC-IPP, which employs Monte Carlo integration. Both IPP algorithms adaptively balance efficiency and accuracy in proximal operator estimation, achieving strong performance and surpassing established solvers across diverse benchmark functions and applications. Together, these works advance first-order nonconvex optimization for deep learning and zeroth-order global optimization in scientific computing.
9:50-10:35
Jiajia Yu, Phillip Griffiths Assistant Research Professor, Duke University
Bio: Jiajia Yu is a Phillip Griffiths Assistant Research Professor in the Department of Mathematics at Duke University. Her research lies at the intersection of scientific machine learning, mean-field games, and optimal transport. She received her Ph.D. in Mathematics from Rensselaer Polytechnic Institute and her B.Sc. in Mathematics from Beijing Normal University.
Title: Learning in Mean-Field Games
Abstract: Mean-field games (MFGs) study systems with a continuum of indistinguishable, non-cooperative agents, with applications ranging from physical, biological, financial, and social systems to more recent connections with reinforcement learning and generative modeling. In these models, an individual’s optimal control depends on the evolving population distribution, and a central object of interest is the mean-field Nash equilibrium (MFNE), where individual behavior is consistent with the resulting population dynamics. Computing the MFNE leads to a highly nonlinear problem and is particularly challenging in the high-dimensional settings that arise in many applications.
In this talk, I will present our recent work on developing a scalable, structure-preserving solver for MFNE. I will first highlight the structure of MFNEs through the concept of best response, and show how this perspective clarifies both the equilibrium problem and the behavior of the fictitious play algorithm. Motivated by these insights, I will introduce a Lagrangian reformulation and use flow-matching ideas from machine learning to adapt fictitious play for scalable high-dimensional computation. If time permits, I will conclude by discussing applications, recent progress, and many exciting open problems in inverse mean-field games.
This talk is based on joint work with Xiuyuan Cheng, Jian-Guo Liu, and Hongkai Zhao at Duke University, and Junghwan Lee and Yao Xie at the Georgia Institute of Technology.
