Generalization of GANs under Lipschitz continuity and data augmentation

Generative adversarial networks (GANs) have been being widely used in various applications. Arguably, GANs are really complex, and little has been known about their generalization. In this paper, we make a comprehensive analysis about generalization of GANs. We decompose the generalization error into an explicit composition: generator error + discriminator error + optimization error. The first two errors show the capacity of the player's families, are irreducible and optimizer-independent. We then provide both uniform and non-uniform generalization bounds in different scenarios, thanks to our new bridge between Lipschitz continuity and generalization. Our bounds overcome some major limitations of existing ones. In particular, our bounds show that penalizing the zero- and first-order informations of the GAN loss will improve generalization, answering the long mystery of why imposing a Lipschitz constraint can help GANs perform better in practice. Finally, we show why data augmentation penalizes the zero- and first-order informations of the loss, helping the players generalize better, and hence explaining the highly successful use of data augmentation for GANs.