We are interested in the design of generative adversarial networks. The training of these mathematical structures requires the definition of proper min-max optimization problems. We propose a simple methodology for constructing such problems assuring, at the same time, that they provide the correct answer. We give characteristic examples developed by our method, some of which can be recognized from other applications and some introduced for the first time. We compare various possibilities by applying them to well known datasets using neural networks of different configurations and sizes.

Designing GANs: A Likelihood Ratio Approach