Title: “Solving” a class of nonconvx min-max optimization problems" 

Abstract: Recent applications that arise in machine learning have surged significant interest in solving min-max optimization problems. This problem has been extensively studied in the convex-concave regime for which a globally optimal solution can be computed efficiently. In the nonconvex regime, on the other hand, most problems cannot be solved to any reasonable notion of stationarity. In this talk, we present different classes of smooth nonconvex min-max problems that can be solved efficiently up to first-order stationarity of its Moreau envelope. In particular, we propose efficient algorithms for finding (first-order) stationary solutions to nonconvex min-max problems classes when the inner maximization problem is concave or when the diameter of the constraint set for the inner maximization problem is "small". We also discuss the validity of our assumptions in various applications and evaluate the performance of our algorithms on different applications including training adversarial robust neural networks, fair machine learning, data imputation, and training generative adversarial networks.

Bio: Meisam Razaviyayn is an assistant professor of Industrial and Systems Engineering, Electrical Engineering, and Computer Science at the University of Southern California. His research interests include the design and analysis of optimization algorithms for modern problems arising in machine learning applications. His contributions to the field of optimization were recognized through awards such as Signal Processing Society Young Author Best PaperAward, ICCM Best Paper Award in Mathematics, IEEE Data Science Workshop Best Paper Award, and the 3M NTFA award, and AFOSR Young Investigator Prize.