A Unifying Generator Loss Function for Generative Adversarial Networks

A unifying alpha-parametrized generator loss function is introduced for a dual-objective generative adversarial network (GAN) that uses a canonical (or classical) discriminator loss function such as the one in the original GAN (VanillaGAN) system. The generator loss function is based on a symmetric class probability estimation type function, L-alpha, and the resulting GAN system is termed L-alpha-GAN. Under an optimal discriminator, it is shown that the generator's optimization problem consists of minimizing a Jensen-f(alpha)-divergence, a natural generalization of the Jensen-Shannon divergence, where f(alpha) is a convex function expressed in terms of the loss function L-alpha. It is also demonstrated that this L-alpha-GAN problem recovers as special cases a number of GAN problems in the literature, including VanillaGAN, least squares GAN (LSGAN), least kth-order GAN (LkGAN), and the recently introduced (alpha(D),alpha(G))-GAN with alpha(D)=1. Finally, experimental results are provided for three datasets-MNIST, CIFAR-10, and Stacked MNIST-to illustrate the performance of various examples of the L-alpha-GAN system.