Objective functions

To create a generator network that generates images that are similar to real images, we try to increase the similarity of the data generated by the generator to real data. To measure the similarity, we use objective functions. Both networks have their own objective functions and during the training, they try to minimize their respective objective functions. The following equation represents the final objective function for GANs:

In the preceding equation,  is the discriminator model,  is the generator model,  is the real data distribution,  is the distribution of the data generated by the generator, and  is the expected output. 

During training, D (the Discriminator) wants to maximize the whole output and G (the Generator) wants to minimize it, thereby training a GAN to reach to an equilibrium between the generator and discriminator network. When it reaches an equilibrium, we say that the model has converged. This equilibrium is the Nash equilibrium. Once the training is complete, we get a generator model that is capable of generating realistic-looking images.