Title: GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium,
Abstract: Generative Adversarial Networks (GANs) excel at creating realistic images
with complex models for which maximum likelihood is infeasible. However, the
convergence of GAN training has still not been proved. We propose a two
time-scale update rule (TTUR) for training GANs with stochastic gradient
descent on arbitrary GAN loss functions. TTUR has an individual learning rate
for both the discriminator and the generator. Using the theory of stochastic
approximation, we prove that the TTUR converges under mild assumptions to a
stationary local Nash equilibrium. The convergence carries over to the popular
Adam optimization, for which we prove that it follows the dynamics of a heavy
ball with friction and thus prefers flat minima in the objective landscape. For
the evaluation of the performance of GANs at image generation, we introduce the
"Fréchet Inception Distance" (FID) which captures the similarity of generated
images to real ones better than the Inception Score. In experiments, TTUR
improves learning for DCGANs and Improved Wasserstein GANs (WGAN-GP)
outperforming conventional GAN training on CelebA, CIFAR-10, SVHN, LSUN
Bedrooms, and the One Billion Word Benchmark.