  Generative adversarial networks (GANs) are powerful generative models, but
usually suffer from instability and generalization problem which may lead to
poor generations. Most existing works focus on stabilizing the training of the
discriminator while ignoring the generalization properties. In this work, we
aim to improve the generalization capability of GANs by promoting the local
robustness within the small neighborhood of the training samples. We also prove
that the robustness in small neighborhood of training sets can lead to better
generalization. Particularly, we design a robust optimization framework where
the generator and discriminator compete with each other in a
\textit{worst-case} setting within a small Wasserstein ball. The generator
tries to map \textit{the worst input distribution} (rather than a Gaussian
distribution used in most GANs) to the real data distribution, while the
discriminator attempts to distinguish the real and fake distribution
\textit{with the worst perturbation}. We have proved that our robust method can
obtain a tighter generalization upper bound than traditional GANs under mild
assumptions, ensuring a theoretical superiority of RGAN over GANs. A series of
experiments on CIFAR-10, STL-10 and CelebA datasets indicate that our proposed
robust framework can improve on five baseline GAN models substantially and
consistently.
