Solving a class of non-convex min-max games using iterative first order methods

Maher Nouiehed, Maziar Sanjabi, Tianjian Huang, Jason D. Lee, Meisam Razaviyayn

Research output: Contribution to journalConference article

4 Scopus citations

Abstract

Recent applications that arise in machine learning have surged significant interest in solving min-max saddle point games. This problem has been extensively studied in the convex-concave regime for which a global equilibrium solution can be computed efficiently. In this paper, we study the problem in the non-convex regime and show that an e-first order stationary point of the game can be computed when one of the player's objective can be optimized to global optimality efficiently. In particular, we first consider the case where the objective of one of the players satisfies the Polyak-Lojasiewicz (PL) condition. For such a game, we show that a simple multi-step gradient descent-ascent algorithm finds an e-first order stationary point of the problem in Oe(e-2) iterations. Then we show that our framework can also be applied to the case where the objective of the “max-player" is concave. In this case, we propose a multi-step gradient descent-ascent algorithm that finds an e-first order stationary point of the game in Oe(e-3.5) iterations, which is the best known rate in the literature. We applied our algorithm to a fair classification problem of Fashion-MNIST dataset and observed that the proposed algorithm results in smoother training and better generalization.

Original languageEnglish (US)
JournalAdvances in Neural Information Processing Systems
Volume32
StatePublished - 2019
Event33rd Annual Conference on Neural Information Processing Systems, NeurIPS 2019 - Vancouver, Canada
Duration: Dec 8 2019Dec 14 2019

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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