# The Landscape of Nonconvex-Nonconcave Minimax Optimization

@article{Grimmer2020TheLO, title={The Landscape of Nonconvex-Nonconcave Minimax Optimization}, author={Benjamin Grimmer and Haihao Lu and Pratik Worah and Vahab S. Mirrokni}, journal={ArXiv}, year={2020}, volume={abs/2006.08667} }

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…

## 4 Citations

A Unified Single-loop Alternating Gradient Projection Algorithm for Nonconvex-Concave and Convex-Nonconcave Minimax Problems

- Computer ScienceArXiv
- 2020

To the best of the authors' knowledge, this is the first time that a simple and unified single-loop algorithm is developed for solving both nonconvex-( strongly) concave and (strongly) convex-nonconcave minimax problems.

Finding First-Order Nash Equilibria of Zero-Sum Games with the Regularized Nikaido-Isoda Function

- Computer ScienceAISTATS
- 2021

This work proposes an algorithm for finding the FNEs of a two-player zero-sum game, in which the local cost functions can be non-convex, and the players only have access to local stochastic gradients.

An $$O(s^r)$$-resolution ODE framework for understanding discrete-time algorithms and applications to the linear convergence of minimax problems

- Computer Science
- 2021

The proposed O(s)-linear-convergence conditions not only unify the known scenarios when PPM and EGM have linear convergence, but also showcase that these two algorithms exhibit linear convergence in much broader contexts, including when solving a class of nonconvex-nonconcave minimax problems.

The limits of min-max optimization algorithms: convergence to spurious non-critical sets

- Computer ScienceICML
- 2021

This paper characterize the convergence properties of a wide class of zeroth-, first-, and (scalable) second-order methods in non-convex/non-concave problems and shows that these state-of-the-art min-max optimization algorithms may converge with arbitrarily high probability to attractors that are in no way min- max optimal or even stationary.

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