Loss functions of GANs

When should we use L1 norm and when should we use L2 norm to minimize loss functions in GANs?

I assume you mean for reconstruction loss. Typically, L2 loss is used when you want to target outliers for gradient descent, while ignoring “in the ballpark” outputs. You can switch between the two. If using L2, I’d only use it at the beginning, then switch to L1 part way through training.

Otherwise, you should just use BCELoss on the Discriminator.

Depends on your training setup.