Special Seminar – Faculty Candidate Ben Grimmer

Title – The Landscape of the Proximal Point Method for Nonconvex-Nonconcave Minimax Optimization
Abstract
Minimax optimization has become a central tool for modern machine learning with applications in generative adversarial networks, robust training, reinforcement learning, etc. These applications are often nonconvex-nonconcave, but the existing theory is unable to identify and deal with the fundamental difficulties this poses. In this talk, we will overcome these limitations, describing the convergence landscape of the classic proximal point method on nonconvex-nonconcave minimax problems. Our key theoretical insight lies in identifying a modified objective, generalizing the Moreau envelope, that smoothes the original objective and convexifies and concavifies it based on the interaction between the minimizing and maximizing variables. When interaction is sufficiently strong, we derive global linear convergence guarantees. When interaction is weak, we derive local linear convergence guarantees under proper initialization. Between these two settings, we show undesirable behaviors like divergence and cycling can occur.
Bio:  Benjamin Grimmer is a PhD student in Operations Research at Cornell University.  He received his BS and MS degrees in Computer Science from Illinois Institute of Technology.  His research focuses on  theoretical foundations of optimization.
Please email Meg Tully – [email protected] for more information