2018

Solving Non-Convex Non-Concave Min-Max Games Under Polyak-{\L}ojasiewicz Condition

Sanjabi, Maziar, Razaviyayn, Meisam, Lee, Jason D.

Understand

In this short note, we consider the problem of solving a min-max zero-sum game.

  • This problem has been extensively studied in the convex-concave regime where the global solution can be computed efficiently.
  • Recently, there have also been developments for finding the first order stationary points of the game when one of the player's objective is concave or (weakly) concave.
  • This work focuses on the non-convex non-concave regime where the objective of one of the players satisfies Polyak-{\L}ojasiewicz (PL) Condition.

Built on

  • On a theorem of danskin with an application to a theorem of von neumann-sion

    P. Bernhard and A. Rapaport · 1995

    Earlier work this paper cites.

  • Degenerate nonlinear programming with a quadratic growth condition

    M. Anitescu · 2000

    Earlier work this paper cites.

  • Introductory lectures on convex optimization: A basic course

    Y. Nesterov · 2013

    Earlier work this paper cites.

Similar

  • Linear convergence of gradient and proximal-gradient methods under the polyak-łojasiewicz condition

    H. Karimi, J. Nutini, and M. Schmidt · 2016

    Cited alongside, same era.

  • A unified distributed algorithm for non-cooperative games., 2016

    J. S. Pang and M. Razaviyayn · 2016

    Cited alongside, same era.

Then

  • Lower bounds for finding stationary points i

    Original

    Y. Carmon, J. C. Duchi, O. Hinder, and A. Sidford · 2017

    Later among the works it cites.

  • On the convergence and robustness of training gans with regularized optimal transport

    M. Sanjabi, J. Ba, M. Razaviyayn, and J. D. Lee · 2018

    Closest in time.

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