Gradient descent GAN optimization is locally stable
This addresses the optimization instability problem in GANs for researchers and practitioners, offering a theoretical foundation and practical solution, though it is incremental as it builds on existing GAN frameworks.
The paper analyzes gradient descent optimization in GANs, proving that equilibrium points are locally asymptotically stable for traditional GANs under certain conditions, while Wasserstein GANs can exhibit non-convergent limit cycles, and proposes a regularization term to ensure local stability for both types, showing practical improvements in convergence and mode collapse.
Despite the growing prominence of generative adversarial networks (GANs), optimization in GANs is still a poorly understood topic. In this paper, we analyze the "gradient descent" form of GAN optimization i.e., the natural setting where we simultaneously take small gradient steps in both generator and discriminator parameters. We show that even though GAN optimization does not correspond to a convex-concave game (even for simple parameterizations), under proper conditions, equilibrium points of this optimization procedure are still \emph{locally asymptotically stable} for the traditional GAN formulation. On the other hand, we show that the recently proposed Wasserstein GAN can have non-convergent limit cycles near equilibrium. Motivated by this stability analysis, we propose an additional regularization term for gradient descent GAN updates, which \emph{is} able to guarantee local stability for both the WGAN and the traditional GAN, and also shows practical promise in speeding up convergence and addressing mode collapse.