Speaker

Dr. Afrooz Jalilzadeh, Assistant Professor, Department of Systems and Industrial Engineering, University of Arizona

Abstract

Game theory and variational inequalities (VIs) provide powerful frameworks for modeling and solving decision-making problems in complex systems. In this talk, we address two key challenges: stochastic VIs and finite-sum structured VIs. First, we focus on monotone stochastic VIs with many functional constraints. Motivated by the limitations of projected stochastic approximation methods, we propose a single-timescale randomized Lagrangian multiplier scheme that combines primal stochastic approximation with dual randomized block-coordinate updates, achieving provable convergence rates. This method also solves minimax problems and Nash games with jointly convex coupling constraints. Second, we tackle finite-sum structured VIs, critical in optimization and machine learning. We introduce a unified stochastic variance-reduced algorithm that employs the Bregman distance function to address both monotone and non-monotone VIs. Our approach guarantees optimal convergence for monotone settings and significantly improves complexity for a structured subclass of non-monotone problems. Together, these contributions advance scalable algorithms for stochastic and finite-sum VIs, with broad applications in machine learning and game theory.

Bio

Dr. Jalilzadeh is an Assistant Professor in the Department of Systems and Industrial Engineering at the University of Arizona. She earned a bachelor’s degree in Mathematics from the University of Tehran and a Ph.D. in Industrial Engineering and Operations Research from Pennsylvania State University. Her research focuses on developing and analyzing stochastic approximation methods to address stochastic optimization and variational inequality problems, with applications in machine learning and game theory. Her work has been supported by the National Science Foundation and the Arizona Technology and Research Initiative Fund, and she has received several teaching awards, including the Gerald J. Swanson Prize for Teaching Excellence from the University of Arizona.

For more information, you can visit her website.