Composite Functional Gradient Learning of Generative Adversarial Models

Generative adversarial networks (GAN) have become popular for generating data that mimic observations by learning a suitable variable transformation from a random variable. However, empirically, GAN is known to suffer from instability. Also, the theory provided based on the minimax optimization formulation of GAN cannot explain the widely-used practical procedure that uses the so-called logd trick. This paper provides a different theoretical foundation for generative adversarial methods which does not rely on the minimax formulation. We show that with a strong discriminator, it is possible to learn a good variable transformation via functional gradient learning, which updates the functional definition of a generator model, instead of updating only the model parameters as in GAN. The theory guarantees that the learned generator improves the KL-divergence between the probability distributions of real data and generated data after each functional gradient step, until the KL-divergence converges to zero. This new point of view leads to enhanced stable procedures for training generative models that can utilize arbitrary learning algorithms. It also gives a new theoretical insight into the original GAN procedure both with and without the logd trick. Empirical results are shown on image generation to illustrate the effectiveness of our new method.