# Fictitious GAN: Training GANs with Historical Models

arXiv: https://arxiv.org/abs/1803.08647 · HTML: https://mlsanity.com/paper/1803.08647/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2018.

## Built on by (most cited first, 7 of 7)

- [FL Games: A Federated Learning Framework for Distribution Shifts](https://mlsanity.com/paper/2211.00184/) (2022)
- [Game of GANs: Game-Theoretical Models for Generative Adversarial Networks](https://mlsanity.com/paper/2106.06976/) (2021)
- [Boundary of Distribution Support Generator (BDSG): Sample Generation on the Boundary](https://mlsanity.com/paper/2107.09950/) (2021)
- [Fuzzy Generative Adversarial Networks](https://mlsanity.com/paper/2110.14588/) (2021)
- [Unified Policy Optimization for Continuous-action Reinforcement Learning in Non-stationary Tasks and Games](https://mlsanity.com/paper/2208.09452/) (2022)
- [FL Games: A federated learning framework for distribution shifts](https://mlsanity.com/paper/2205.11101/) (2022)
- [Nested Annealed Training Scheme for Generative Adversarial Networks](https://mlsanity.com/paper/2501.11318/) (2025)

## Abstract (arXiv)

Generative adversarial networks (GANs) are powerful tools for learning generative models. In practice, the training may suffer from lack of convergence. GANs are commonly viewed as a two-player zero-sum game between two neural networks. Here, we leverage this game theoretic view to study the convergence behavior of the training process. Inspired by the fictitious play learning process, a novel training method, referred to as Fictitious GAN, is introduced. Fictitious GAN trains the deep neural networks using a mixture of historical models. Specifically, the discriminator (resp. generator) is updated according to the best-response to the mixture outputs from a sequence of previously trained generators (resp. discriminators). It is shown that Fictitious GAN can effectively resolve some convergence issues that cannot be resolved by the standard training approach. It is proved that asymptotically the average of the generator outputs has the same distribution as the data samples.