  Generative adversarial networks (GANs) are a class of generative models,
known for producing accurate samples. The key feature of GANs is that there are
two antagonistic neural networks: the generator and the discriminator. The main
bottleneck for their implementation is that the neural networks are very hard
to train. One way to improve their performance is to design reliable algorithms
for the adversarial process. Since the training can be cast as a stochastic
Nash equilibrium problem, we rewrite it as a variational inequality and
introduce an algorithm to compute an approximate solution. Specifically, we
propose a stochastic relaxed forward-backward algorithm for GANs. We prove that
when the pseudogradient mapping of the game is monotone, we have convergence to
an exact solution or in a neighbourhood of it.
