# Revisiting GANs by Best-Response Constraint: Perspective, Methodology, and Application

arXiv: https://arxiv.org/abs/2205.10146 · HTML: https://mlsanity.com/paper/2205.10146/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 30 references that are in the map.
- First posted on arXiv 20 May 2022.

## Builds on (most cited first, 21 of 21)

- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Least Squares Generative Adversarial Networks](https://mlsanity.com/paper/1611.04076/) (2016)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Optimizing Millions of Hyperparameters by Implicit Differentiation](https://mlsanity.com/paper/1911.02590/) (2019)
- [Forward and Reverse Gradient-Based Hyperparameter Optimization](https://mlsanity.com/paper/1703.01785/) (2017)
- [Hyperparameter optimization with approximate gradient](https://mlsanity.com/paper/1602.02355/) (2016)
- [Unrolled Generative Adversarial Networks](https://mlsanity.com/paper/1611.02163/) (2016)
- [Controllable Text-to-Image Generation](https://mlsanity.com/paper/1909.07083/) (2019)
- [Mode Regularized Generative Adversarial Networks](https://mlsanity.com/paper/1612.02136/) (2016)
- [The Complexity of Constrained Min-Max Optimization](https://mlsanity.com/paper/2009.09623/) (2020)
- [Rebooting ACGAN: Auxiliary Classifier GANs with Stable Training](https://mlsanity.com/paper/2111.01118/) (2021)
- [Connecting Generative Adversarial Networks and Actor-Critic Methods](https://mlsanity.com/paper/1610.01945/) (2016)
- [Latent Constraints: Learning to Generate Conditionally from Unconditional Generative Models](https://mlsanity.com/paper/1711.05772/) (2017)
- [AdaGAN: Boosting Generative Models](https://mlsanity.com/paper/1701.02386/) (2017)
- [On Computation and Generalization of Generative Adversarial Imitation Learning](https://mlsanity.com/paper/2001.02792/) (2020)
- [A General Descent Aggregation Framework for Gradient-based Bi-level Optimization](https://mlsanity.com/paper/2102.07976/) (2021)
- [A 3D GAN for Improved Large-pose Facial Recognition](https://mlsanity.com/paper/2012.10545/) (2020)
- [Global Convergence to the Equilibrium of GANs using Variational Inequalities](https://mlsanity.com/paper/1808.01531/) (2018)

## Built on by (most cited first, 3 of 3)

- [Bi-level Dynamic Learning for Jointly Multi-modality Image Fusion and Beyond](https://mlsanity.com/paper/2305.06720/) (2023)
- [PAIF: Perception-Aware Infrared-Visible Image Fusion for Attack-Tolerant Semantic Segmentation](https://mlsanity.com/paper/2308.03979/) (2023)
- [Bilevel Generative Learning for Low-Light Vision](https://mlsanity.com/paper/2308.03381/) (2023)

## Abstract (arXiv)

In past years, the minimax type single-level optimization formulation and its variations have been widely utilized to address Generative Adversarial Networks (GANs). Unfortunately, it has been proved that these alternating learning strategies cannot exactly reveal the intrinsic relationship between the generator and discriminator, thus easily result in a series of issues, including mode collapse, vanishing gradients and oscillations in the training phase, etc. In this work, by investigating the fundamental mechanism of GANs from the perspective of hierarchical optimization, we propose Best-Response Constraint (BRC), a general learning framework, that can explicitly formulate the potential dependency of the generator on the discriminator. Rather than adopting these existing time-consuming bilevel iterations, we design an implicit gradient scheme with outer-product Hessian approximation as our fast solution strategy. Noteworthy, we demonstrate that even with different motivations and formulations, a variety of existing GANs ALL can be uniformly improved by our flexible BRC methodology. Extensive quantitative and qualitative experimental results verify the effectiveness, flexibility and stability of our proposed framework.