# GDA-AM: On the effectiveness of solving minimax optimization via Anderson Acceleration

arXiv: https://arxiv.org/abs/2110.02457 · HTML: https://mlsanity.com/paper/2110.02457/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 64 references that are in the map.
- First posted on arXiv 6 Oct 2021.

## Builds on (most cited first, 30 of 36)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [Training GANs with Optimism](https://mlsanity.com/paper/1711.00141/) (2017)
- [Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methods](https://mlsanity.com/paper/1902.08297/) (2019)
- [A Variational Inequality Perspective on Generative Adversarial Networks](https://mlsanity.com/paper/1802.10551/) (2018)
- [A Unified Analysis of Extra-gradient and Optimistic Gradient Methods for Saddle Point Problems: Proximal Point Approach](https://mlsanity.com/paper/1901.08511/) (2019)
- [Optimistic mirror descent in saddle-point problems: Going the extra (gradient) mile](https://mlsanity.com/paper/1807.02629/) (2018)
- [The Numerics of GANs](https://mlsanity.com/paper/1705.10461/) (2017)
- [On the convergence of single-call stochastic extra-gradient methods](https://mlsanity.com/paper/1908.08465/) (2019)
- [Stochastic Recursive Gradient Descent Ascent for Stochastic Nonconvex-Strongly-Concave Minimax Problems](https://mlsanity.com/paper/2001.03724/) (2020)
- [Efficient Algorithms for Smooth Minimax Optimization](https://mlsanity.com/paper/1907.01543/) (2019)
- [The Unusual Effectiveness of Averaging in GAN Training](https://mlsanity.com/paper/1806.04498/) (2018)
- [Negative Momentum for Improved Game Dynamics](https://mlsanity.com/paper/1807.04740/) (2018)
- [A Single-Loop Smoothed Gradient Descent-Ascent Algorithm for Nonconvex-Concave Min-Max Problems](https://mlsanity.com/paper/2010.15768/) (2020)
- [A Unified Single-loop Alternating Gradient Projection Algorithm for Nonconvex-Concave and Convex-Nonconcave Minimax Problems](https://mlsanity.com/paper/2006.02032/) (2020)
- [Efficient Search of First-Order Nash Equilibria in Nonconvex-Concave Smooth Min-Max Problems](https://mlsanity.com/paper/2002.07919/) (2020)
- [On Finding Local Nash Equilibria (and Only Local Nash Equilibria) in Zero-Sum Games](https://mlsanity.com/paper/1901.00838/) (2019)
- [On Solving Minimax Optimization Locally: A Follow-the-Ridge Approach](https://mlsanity.com/paper/1910.07512/) (2019)
- [Competitive Gradient Descent](https://mlsanity.com/paper/1905.12103/) (2019)
- [Near-optimal Local Convergence of Alternating Gradient Descent-Ascent for Minimax Optimization](https://mlsanity.com/paper/2102.09468/) (2021)
- [Local Saddle Point Optimization: A Curvature Exploitation Approach](https://mlsanity.com/paper/1805.05751/) (2018)
- [Last iterate convergence in no-regret learning: constrained min-max optimization for convex-concave landscapes](https://mlsanity.com/paper/2002.06768/) (2020)
- [Ridge Rider: Finding Diverse Solutions by Following Eigenvectors of the Hessian](https://mlsanity.com/paper/2011.06505/) (2020)

## Abstract (arXiv)

Many modern machine learning algorithms such as generative adversarial networks (GANs) and adversarial training can be formulated as minimax optimization. Gradient descent ascent (GDA) is the most commonly used algorithm due to its simplicity. However, GDA can converge to non-optimal minimax points. We propose a new minimax optimization framework, GDA-AM, that views the GDAdynamics as a fixed-point iteration and solves it using Anderson Mixing to con-verge to the local minimax. It addresses the diverging issue of simultaneous GDAand accelerates the convergence of alternating GDA. We show theoretically that the algorithm can achieve global convergence for bilinear problems under mild conditions. We also empirically show that GDA-AMsolves a variety of minimax problems and improves GAN training on several datasets