Nonconvex Min-Max Optimization: Applications, Challenges, and Recent Theoretical Advances

Meisam Razaviyayn, Tianjian Huang, Songtao Lu, Maher Nouiehed, Maziar Sanjabi, Mingyi Hong

Abstract: The min-max optimization problem, also known as the <;i>saddle point problem<;/i>, is a classical optimization problem that is also studied in the context of zero-sum games. Given a class of objective functions, the goal is to find a value for the argument that leads to a small objective value even for the worst-case function in the given class. Min-max optimization problems have recently become very popular in a wide range of signal and data processing applications, such as fair beamforming, training generative adversarial networks (GANs), and robust machine learning (ML), to just name a few.