Revisiting GAN with Bayes-Optimal Discrimination
TL;DR
An adversarial game in which the discriminator tightens this bound and the generator maximizes it is formulated, and it is shown that, under balanced class priors, the population game is equivalent to minimizing total variation between the data and generator distributions.
Abstract
We approach generative adversarial network (GAN) training from its original real-versus-fake classification viewpoint, replacing the cross-entropy discriminator objective with an upper bound on the Bayes error rate (BER). Using the Bayes optimal learning threshold (BOLT) loss, we formulate an adversarial game in which the discriminator tightens this bound and the generator maximizes it. We characterize the unrestricted optimal discriminator and show that, under balanced class priors, the population game is equivalent to minimizing total variation between the data and generator distributions. Restricting the bounded discriminator to be 1-Lipschitz yields BOLT-GAN. For balanced priors and the full discriminator class, we establish upper and lower bounds relating its population discrepancy to Wasserstein-1 distance on bounded domains. Controlled experiments on four image-generation benchmarks show improved sample quality and coverage over WGAN-GP under matched architectures, optimization settings, and gradient penalties. At a common 20-epoch budget, BOLT-GAN reduces Fr\'echet Inception Distance (FID) from 60.0 to 44.2 on CIFAR-10 and from 102.5 to 28.4 on LSUN Bedroom-64.
