The Landscape of Nonconvex-Nonconcave Minimax Optimization

by   Benjamin Grimmer, et al.

Minimax optimization has become a central tool for modern machine learning with applications in robust optimization, game theory and training GANs. These applications are often nonconvex-nonconcave, but the existing theory is unable to identify and deal with the fundamental difficulties posed by nonconvex-nonconcave structures. We break this historical barrier by identifying three regions of nonconvex-nonconcave bilinear minimax problems and characterizing their different solution paths. For problems where the interaction between the agents is sufficiently strong, we derive global linear convergence guarantees. Conversely when the interaction between the agents is fairly weak, we derive local linear convergence guarantees. Between these two settings, we show that limiting cycles may occur, preventing the convergence of the solution path.



page 1

page 2

page 3

page 4


Federated Minimax Optimization: Improved Convergence Analyses and Algorithms

In this paper, we consider nonconvex minimax optimization, which is gain...

On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems

We consider nonconvex-concave minimax problems, _x_y∈Y f(x, y), where f ...

Limiting Behaviors of Nonconvex-Nonconcave Minimax Optimization via Continuous-Time Systems

Unlike nonconvex optimization, where gradient descent is guaranteed to c...

Uniform Convergence and Generalization for Nonconvex Stochastic Minimax Problems

This paper studies the uniform convergence and generalization bounds for...

Global Convergence and Variance-Reduced Optimization for a Class of Nonconvex-Nonconcave Minimax Problems

Nonconvex minimax problems appear frequently in emerging machine learnin...

Newton-type Methods for Minimax Optimization

Differential games, in particular two-player sequential games (a.k.a. mi...

Game Theory on the Ground: The Effect of Increased Patrols on Deterring Poachers

Applications of artificial intelligence for wildlife protection have foc...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.