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.
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