Euler-Lagrange Analysis of Generative Adversarial Networks

We consider Generative Adversarial Networks (GANs) and address the underlying functional optimization problem ab initio within a variational setting. Strictly speaking, the optimization of the generator and discriminator functions must be carried out in accordance with the Euler-Lagrange conditions, which become particularly relevant in scenarios where the optimization cost involves regularizers comprising the derivatives of these functions. Considering Wasserstein GANs (WGANs) with a gradient-norm penalty, we show that the optimal discriminator is the solution to a Poisson differential equation. In …

analysis become cost derivatives functional gans generative generative adversarial networks generator networks optimization speaking