I've seen an advice about GAN implementation, that there should be different optimizers for generator (G) and discriminator (D). As I understand, it depends on how fast each model (G and D) convergences. I'd like to clarify this question. Why is it possible to say, that, for example, GSD has to be chosen for D and Adam for G only and not vice verse? (Intuitive or mathematical explanations are welcomed both)
Maybe you can share the link to this advice, so we get the context or arguments, because it doesn’t make a lot of sense to me.
You specifically ask why it’s possible to choose different optimizers. The only requirement that the relation between the discriminator and the generator must meet, is that the discriminator must be able to handle the generator output. Everything else can be different, including the optimizer, prediction algorithm, any regularization, and so on. You could have a neural net for the generator and Mechanical Turk could be your discriminator.
There is something to be said for having different algorithms or architectures between the generator and the discriminator, essentially so the discriminator is able to pick up on the weaknesses of the generator. (Because they won’t share the same weaknesses, hopefully.) But to have everything the same and change only the optimizer? I don’t see the point in that.
Generative Adversarial Networks are always implemented as a couple of models: the generator and the discriminator. They are meant to play against each other, in order to make them improve through competition. That said, nothing blocks scientists to try different optimizations for the two Networks. Even if they play and learn at the same time, they are still separate models, and it's only the generator that later is sent to production.
Certainly two different optimizer objects have to be instantiated, because different Networks (a generator-decoder and a classifier) have different architectures and parameters and are trained differently. But whether they are both Adam or two different algorithms, that's completely up to your choice.