  We investigate the training and performance of generative adversarial
networks using the Maximum Mean Discrepancy (MMD) as critic, termed MMD GANs.
As our main theoretical contribution, we clarify the situation with bias in GAN
loss functions raised by recent work: we show that gradient estimators used in
the optimization process for both MMD GANs and Wasserstein GANs are unbiased,
but learning a discriminator based on samples leads to biased gradients for the
generator parameters. We also discuss the issue of kernel choice for the MMD
critic, and characterize the kernel corresponding to the energy distance used
for the Cramer GAN critic. Being an integral probability metric, the MMD
benefits from training strategies recently developed for Wasserstein GANs. In
experiments, the MMD GAN is able to employ a smaller critic network than the
Wasserstein GAN, resulting in a simpler and faster-training algorithm with
matching performance. We also propose an improved measure of GAN convergence,
the Kernel Inception Distance, and show how to use it to dynamically adapt
learning rates during GAN training.
