The objective function equality property of infoGAN for two-layer network

Information Maximizing Generative Adversarial Network (infoGAN) can be understood as a minimax problem involving two networks: discriminators and generators with mutual information functions. The infoGAN incorporates various components, including latent variables, mutual information, and objective function. This research demonstrates that the two objective functions in infoGAN become equivalent as the discriminator and generator sample size approaches infinity. This equivalence is established by considering the disparity between the empirical and population versions of the objective function. The bound on this difference is determined by the Rademacher complexity of the discriminator and generator function class. Furthermore, the utilization of a two-layer network for both the discriminator and generator, featuring Lipschitz and non-decreasing activation functions, validates this equality