A Unifying Generator Loss Function for Generative Adversarial Networks
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A unifying α-parametrized generator loss function is introduced for a dual-objective generative adversarial network (GAN), which 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_α, and the resulting GAN system is termed ℒ_α-GAN. Under an optimal discriminator, it is shown that the generator's optimization problem consists of minimizing a Jensen-f_α-divergence, a natural generalization of the Jensen-Shannon divergence, where f_α is a convex function expressed in terms of the loss function ℒ_α. It is also demonstrated that this ℒ_α-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 (α_D,α_G)-GAN with α_D=1. Finally, experimental results are conducted on three datasets, MNIST, CIFAR-10, and Stacked MNIST to illustrate the performance of various examples of the ℒ_α-GAN system.
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