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We relate the minimax game of generative adversarial networks (GANs) tofinding the saddle points of the Lagrangian function for a convex optimizationproblem, where the discriminator outputs and the distribution of generatoroutputs play the roles of primal variables and dual variables, respectively.This formulation shows the connection between the standard GAN training processand the primal-dual subgradient methods for convex optimization. The inherentconnection does not only provide a theoretical convergence proof for trainingGANs in the function space, but also inspires a novel objective function fortraining. The modified objective function forces the distribution of generatoroutputs to be updated along the direction according to the primal-dualsubgradient methods. A toy example shows that the proposed method is able toresolve mode collapse, which in this case cannot be avoided by the standard GANor Wasserstein GAN. Experiments on both Gaussian mixture synthetic data andreal-world image datasets demonstrate the performance of the proposed method ongenerating diverse samples.

Training Generative Adversarial Networks via Primal-Dual Subgradient Methods: A Lagrangian Perspective on GAN