# Approximation and Convergence Properties of Generative Adversarial Learning

arXiv: https://arxiv.org/abs/1705.08991 · HTML: https://mlsanity.com/paper/1705.08991/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2017.

## Built on by (most cited first, 28 of 28)

- [Generative Adversarial Neural Operators](https://mlsanity.com/paper/2205.03017/) (2022)
- [KALE Flow: A Relaxed KL Gradient Flow for Probabilities with Disjoint Support](https://mlsanity.com/paper/2106.08929/) (2021)
- [MaGNET: Uniform Sampling from Deep Generative Network Manifolds Without Retraining](https://mlsanity.com/paper/2110.08009/) (2021)
- [A Neural Tangent Kernel Perspective of GANs](https://mlsanity.com/paper/2106.05566/) (2021)
- [Constrained Policy Optimization with Explicit Behavior Density for Offline Reinforcement Learning](https://mlsanity.com/paper/2301.12130/) (2023)
- [A survey on GANs for computer vision: Recent research, analysis and taxonomy](https://mlsanity.com/paper/2203.11242/) (2022)
- [Ten Years of Generative Adversarial Nets (GANs): A survey of the state-of-the-art](https://mlsanity.com/paper/2308.16316/) (2023)
- [A likelihood approach to nonparametric estimation of a singular distribution using deep generative models](https://mlsanity.com/paper/2105.04046/) (2021)
- [Realizing GANs via a Tunable Loss Function](https://mlsanity.com/paper/2106.05232/) (2021)
- [Dual-Scale Single Image Dehazing Via Neural Augmentation](https://mlsanity.com/paper/2209.05913/) (2022)
- [DigGAN: Discriminator gradIent Gap Regularization for GAN Training with Limited Data](https://mlsanity.com/paper/2211.14694/) (2022)
- [Minimax Optimality (Probably) Doesn't Imply Distribution Learning for GANs](https://mlsanity.com/paper/2201.07206/) (2022)
- [Matching aggregate posteriors in the variational autoencoder](https://mlsanity.com/paper/2311.07693/) (2023)
- [α-GAN: Convergence and Estimation Guarantees](https://mlsanity.com/paper/2205.06393/) (2022)
- [Addressing GAN Training Instabilities via Tunable Classification Losses](https://mlsanity.com/paper/2310.18291/) (2023)
- [Reducing Training Sample Memorization in GANs by Training with Memorization Rejection](https://mlsanity.com/paper/2210.12231/) (2022)
- [Statistical inference for generative adversarial networks and other minimax problems](https://mlsanity.com/paper/2104.10601/) (2021)
- [Statistical Regeneration Guarantees of the Wasserstein Autoencoder with Latent Space Consistency](https://mlsanity.com/paper/2110.03995/) (2021)
- [Non-Asymptotic Error Bounds for Bidirectional GANs](https://mlsanity.com/paper/2110.12319/) (2021)
- [Training Wasserstein GANs without gradient penalties](https://mlsanity.com/paper/2110.14150/) (2021)
- [Asymptotic Statistical Analysis of f-divergence GAN](https://mlsanity.com/paper/2209.06853/) (2022)
- [Statistical Error Bounds for GANs with Nonlinear Objective Functionals](https://mlsanity.com/paper/2406.16834/) (2024)
- [MGHF: Multi-Granular High-Frequency Perceptual Loss for Image Super-Resolution](https://mlsanity.com/paper/2411.13548/) (2024)
- [MCGAN: Enhancing GAN Training with Regression-Based Generator Loss](https://mlsanity.com/paper/2405.17191/) (2024)
- [Cross-Domain Policy Transfer by Representation Alignment via Multi-Domain Behavioral Cloning](https://mlsanity.com/paper/2407.16912/) (2024)
- [On the Nash equilibrium of moment-matching GANs for stationary Gaussian processes](https://mlsanity.com/paper/2203.07136/) (2022)
- [Seasoning Generative Models for a Generalization Aftertaste](https://mlsanity.com/paper/2603.18817/) (2026)
- [Nonparametric Deconvolution and Denoising using Simulation Based Inference](https://mlsanity.com/paper/2606.21907/) (2026)

## Abstract (arXiv)

Generative adversarial networks (GAN) approximate a target data distribution by jointly optimizing an objective function through a "two-player game" between a generator and a discriminator. Despite their empirical success, however, two very basic questions on how well they can approximate the target distribution remain unanswered. First, it is not known how restricting the discriminator family affects the approximation quality. Second, while a number of different objective functions have been proposed, we do not understand when convergence to the global minima of the objective function leads to convergence to the target distribution under various notions of distributional convergence. In this paper, we address these questions in a broad and unified setting by defining a notion of adversarial divergences that includes a number of recently proposed objective functions. We show that if the objective function is an adversarial divergence with some additional conditions, then using a restricted discriminator family has a moment-matching effect. Additionally, we show that for objective functions that are strict adversarial divergences, convergence in the objective function implies weak convergence, thus generalizing previous results.