  Generative adversarial networks (GANs) are powerful tools for learning
generative models. In practice, the training may suffer from lack of
convergence. GANs are commonly viewed as a two-player zero-sum game between two
neural networks. Here, we leverage this game theoretic view to study the
convergence behavior of the training process. Inspired by the fictitious play
learning process, a novel training method, referred to as Fictitious GAN, is
introduced. Fictitious GAN trains the deep neural networks using a mixture of
historical models. Specifically, the discriminator (resp. generator) is updated
according to the best-response to the mixture outputs from a sequence of
previously trained generators (resp. discriminators). It is shown that
Fictitious GAN can effectively resolve some convergence issues that cannot be
resolved by the standard training approach. It is proved that asymptotically
the average of the generator outputs has the same distribution as the data
samples.
