  Generative adversarial networks (GANs) generate data based on minimizing a
divergence between two distributions. The choice of that divergence is
therefore critical. We argue that the divergence must take into account the
hypothesis set and the loss function used in a subsequent learning task, where
the data generated by a GAN serves for training. Taking that structural
information into account is also important to derive generalization guarantees.
Thus, we propose to use the discrepancy measure, which was originally
introduced for the closely related problem of domain adaptation and which
precisely takes into account the hypothesis set and the loss function. We show
that discrepancy admits favorable properties for training GANs and prove
explicit generalization guarantees. We present efficient algorithms using
discrepancy for two tasks: training a GAN directly, namely DGAN, and mixing
previously trained generative models, namely EDGAN. Our experiments on toy
examples and several benchmark datasets show that DGAN is competitive with
other GANs and that EDGAN outperforms existing GAN ensembles, such as AdaGAN.
