Optimality Conditions for Nonsmooth Nonconvex-Nonconcave Min-Max Problems and Generative Adversarial Networks

Jie Jiang, Xiaojun Chen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

This paper considers a class of nonsmooth nonconvex-nonconcave min-max problems in machine learning and games. We first provide sufficient conditions for the existence of global minimax points and local minimax points. Next, we establish the first-order and second-order optimality conditions for local minimax points by using directional derivatives. These conditions reduce to smooth minmax
problems with Fréchet derivatives. We apply our theoretical results to generative adversarial networks (GANs) in which two neural networks contest with each other in a game. Examples are used to illustrate applications of the new theory for training GANs.
Original languageEnglish
Pages (from-to)693-722
Number of pages30
JournalSIAM Journal on Mathematics of Data Science
Volume5
Issue number3
DOIs
Publication statusPublished - Sept 2029

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