Error analysis of generative adversarial network
Mahmud Hasan Hailin Sang
The generative adversarial network (GAN) is an important model developed for
high-dimensional distribution learning in recent years. However, there is a
pressing need for a comprehensive method to understand its error convergence
rate. In this research, we focus on studying the error convergence rate of the
GAN model that is based on a class of functions encompassing the discriminator
and generator neural networks. These functions are VC type with bounded
envelope function under our assumptions, enabling the application of the
Talagrand inequality. By employing the Talagrand inequality and Borel-Cantelli
lemma, we establish a tight convergence rate for the error of GAN. This method
can also be applied on existing error estimations of GAN and yields improved
convergence rates. In particular, the error defined with the neural network
distance is a special case error in our definition.