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 that has an individual learning rate for both the discriminator and the generator. We prove that the TTUR converges under mild assumptions to a stationary 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 "Fr\'echet 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, improved Wasserstein GANs, and BEGANs, outperforming conventional GAN training on CelebA, Billion Word Benchmark, and LSUN bedrooms.

本文提出一种基于二次尺度更新规则的GAN训练方法，使用随机逼近理论证明其可以收敛于本地Nash均衡点，并且在图像生成方面的表现优于传统GAN算法，同时提出了一种新的用于评估GAN生成图像质量的指标Fr\'echet Inception Distance。

通过双时间尺度更新规则训练的GAN收敛于局部纳什均衡