# SGD Learns One-Layer Networks in WGANs

arXiv: https://arxiv.org/abs/1910.07030 · HTML: https://mlsanity.com/paper/1910.07030/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2019.

## Built on by (most cited first, 16 of 16)

- [Faster Single-loop Algorithms for Minimax Optimization without Strong Concavity](https://mlsanity.com/paper/2112.05604/) (2021)
- [The Complexity of Nonconvex-Strongly-Concave Minimax Optimization](https://mlsanity.com/paper/2103.15888/) (2021)
- [Two-Timescale Gradient Descent Ascent Algorithms for Nonconvex Minimax Optimization](https://mlsanity.com/paper/2408.11974/) (2024)
- [Understanding Overparameterization in Generative Adversarial Networks](https://mlsanity.com/paper/2104.05605/) (2021)
- [Reversible Gromov-Monge Sampler for Simulation-Based Inference](https://mlsanity.com/paper/2109.14090/) (2021)
- [Learning (Very) Simple Generative Models Is Hard](https://mlsanity.com/paper/2205.16003/) (2022)
- [Solving Min-Max Optimization with Hidden Structure via Gradient Descent Ascent](https://mlsanity.com/paper/2101.05248/) (2021)
- [Generalization Error of GAN from the Discriminator's Perspective](https://mlsanity.com/paper/2107.03633/) (2021)
- [Generalization Bounds of Nonconvex-(Strongly)-Concave Stochastic Minimax Optimization](https://mlsanity.com/paper/2205.14278/) (2022)
- [A Mathematical Framework for Learning Probability Distributions](https://mlsanity.com/paper/2212.11481/) (2022)
- [Minimax Optimality (Probably) Doesn't Imply Distribution Learning for GANs](https://mlsanity.com/paper/2201.07206/) (2022)
- [Dissecting adaptive methods in GANs](https://mlsanity.com/paper/2210.04319/) (2022)
- [WGAN with an Infinitely Wide Generator Has No Spurious Stationary Points](https://mlsanity.com/paper/2102.07541/) (2021)
- [On the Optimization Landscape of Maximum Mean Discrepancy](https://mlsanity.com/paper/2110.13452/) (2021)
- [Why Adversarial Interaction Creates Non-Homogeneous Patterns: A Pseudo-Reaction-Diffusion Model for Turing Instability](https://mlsanity.com/paper/2010.00521/) (2020)
- [On the Nash equilibrium of moment-matching GANs for stationary Gaussian processes](https://mlsanity.com/paper/2203.07136/) (2022)

## Abstract (arXiv)

Generative adversarial networks (GANs) are a widely used framework for learning generative models. Wasserstein GANs (WGANs), one of the most successful variants of GANs, require solving a minmax optimization problem to global optimality, but are in practice successfully trained using stochastic gradient descent-ascent. In this paper, we show that, when the generator is a one-layer network, stochastic gradient descent-ascent converges to a global solution with polynomial time and sample complexity.