Should Discriminator Loss increase or decrease?
Discriminator consist of two loss parts (1st: detect real image as real; 2nd detect fake image as fake). 'Full discriminator loss' is sum of these two parts.
The loss should be as small as possible for both the generator and the discriminator. But there is a catch: the smaller the discriminator loss becomes, the more the generator loss increases and vice versa.
Discriminator loss: Ideally the full discriminator's loss should be around 0.5 for one instance, which would mean the discriminator is GUESSING whether the image is real or fake (e.g. the same as coin toss: you try to guess is it a tail or a head).
Generator loss: Ultimately it should decrease over the next epoch (important: we should choose the optimal number of epoch so as not to overfit our a neural network).
I could recommend this article to understand it better.