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), 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, $\mathcal{L}_\alpha$, and the resulting GAN system is termed $\mathcal{L}_\alpha$-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 $\mathcal{L}_\alpha$. It is also demonstrated that this $\mathcal{L}_\alpha$-GAN problem recovers as special cases a number of GAN problems in the literature, including VanillaGAN, Least Squares GAN (LSGAN), Least $k$th order GAN (L$k$GAN) and the recently introduced $(\alpha_D,\alpha_G)$-GAN with $\alpha_D=1$. Finally, experimental results are conducted on three datasets, MNIST, CIFAR-10, and Stacked MNIST to illustrate the performance of various examples of the $\mathcal{L}_\alpha$-GAN system.