# Stackelberg GAN: Towards Provable Minimax Equilibrium via Multi-Generator Architectures

arXiv: https://arxiv.org/abs/1811.08010 · HTML: https://mlsanity.com/paper/1811.08010/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2018.

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

- [Synaptic Plasticity Models and Bio-Inspired Unsupervised Deep Learning: A Survey](https://mlsanity.com/paper/2307.16236/) (2023)
- [Game of GANs: Game-Theoretical Models for Generative Adversarial Networks](https://mlsanity.com/paper/2106.06976/) (2021)
- [Top-Down Deep Clustering with Multi-generator GANs](https://mlsanity.com/paper/2112.03398/) (2021)
- [Distributed Traffic Synthesis and Classification in Edge Networks: A Federated Self-supervised Learning Approach](https://mlsanity.com/paper/2302.00207/) (2023)
- [Towards convergence to Nash equilibria in two-team zero-sum games](https://mlsanity.com/paper/2111.04178/) (2021)
- [ApproxED: Approximate exploitability descent via learned best responses](https://mlsanity.com/paper/2301.08830/) (2023)
- [Nested Annealed Training Scheme for Generative Adversarial Networks](https://mlsanity.com/paper/2501.11318/) (2025)

## Abstract (arXiv)

We study the problem of alleviating the instability issue in the GAN training procedure via new architecture design. The discrepancy between the minimax and maximin objective values could serve as a proxy for the difficulties that the alternating gradient descent encounters in the optimization of GANs. In this work, we give new results on the benefits of multi-generator architecture of GANs. We show that the minimax gap shrinks to ε as the number of generators increases with rate widetildeO(1/ε). This improves over the best-known result of widetildeO(1/ε2). At the core of our techniques is a novel application of Shapley-Folkman lemma to the generic minimax problem, where in the literature the technique was only known to work when the objective function is restricted to the Lagrangian function of a constraint optimization problem. Our proposed Stackelberg GAN performs well experimentally in both synthetic and real-world datasets, improving Fr'echet Inception Distance by 14.61% over the previous multi-generator GANs on the benchmark datasets.