A Variational Inequality Perspective on Generative Adversarial Networks

If you used our work please consider citing us as:

Gidel, G., Berard, H., Vignoud, G., Vincent, P., & Lacoste-Julien, S. (2019). A variational inequality perspective on generative adversarial networks in ICLR.




Generative adversarial networks (GANs) form a generative modeling approach known for producing appealing samples, but they are notably difficult to train. One common way to tackle this issue has been to propose new formulations of the GAN objective. Yet, surprisingly few studies have looked at optimization methods designed for this adversarial training. In this work, we cast GAN optimization problems in the general variational inequality framework. Tapping into the mathematical programming literature, we counter some common misconceptions about the difficulties of saddle point optimization and propose to extend techniques designed for variational inequalities to the training of GANs. We apply averaging, extrapolation and a computationally cheaper variant that we call extrapolation from the past to the stochastic gradient method (SGD) and Adam.


ICLR, 2019. (ranked 35th, TOP 2.2% submitted papers)

Also accepted as an oral presentation at the Montreal AI Symposium 2018
(TOP 15% of accepted submissions)


Credit to Hugo Berard for the Github folder.


This research was partially supported by the Canada CIFAR AI Chair Program, the Canada Excellence Research Chair in “Data Science for Realtime Decision-making”, by the NSERC Discovery Grant RGPIN-2017-06936, by a Google Focused Research award and Facebook AI Research. Gauthier Gidel would like to acknowledge Benoît Joly and Florestan Martin-Baillon for bringing a fresh point of view on the proof of Proposition 1.

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