I’m a bit confused about this minmax game, especially in regards of the generator and the fact that it’s trying to Maximize the cost, aren’t we always supposed to minimize the cost function ?

You have 2 fighting processes with each other; one tries to minimize and the other one to maximize it so they can counteract each other. This is not the cost function of simple logistic regression model but 2 models at the same time and interrelated to each other!

Basically, the generator wants to maximize the cost *for the discriminator*. The worse the discriminator does at identifying fake images the generator created, the better that means the generator did at creating good fakes.

The goal of the generator is to minimize this loss whereas the discriminator tries to maximize it.

The goal when training GAN architectures is to ﬁnd a *Nash-equilibrium*, i.e., a parameter

assignment in which neither the discriminator nor the generator can improve their utilities unilaterally by deviating current strategy.