Nonconvex Minimax Optimization

Nonconvex minimax optimization focuses on finding saddle points of functions that are nonconvex in one set of variables and concave (or potentially nonconcave) in another, a problem arising frequently in machine learning. Current research emphasizes developing efficient algorithms, such as gradient descent ascent (GDA) variants with adaptive learning rates and two-timescale updates, and analyzing their convergence properties under various assumptions, including Polyak-Łojasiewicz and Kurdyka-Łojasiewicz conditions. These advancements are crucial for improving the training of generative adversarial networks and other machine learning models, particularly in distributed settings like federated learning, where communication efficiency is paramount.