Paper:
Published as a conference paper at ICLR 2018 IMPROVING GANS USING OPTIMAL TRANSPORT
We present Optimal Transport GAN (OT-GAN), a variant of generative adversarial nets minimizing a new metric measuring the distance between the generator distribution and the data distribution. This metric, which we call mini-batch energy distance, combines optimal transport in primal form with an energy distance defined in an adversarially learned feature space, resulting in a highly discriminative distance function with unbiased mini-batch gradients. Experimentally we show OT-GAN to be highly stable when trained with large mini-batches, and we present state-of-the-art results on several popular benchmark problems for image generation.

Review:
There have recently been a set of interesting papers on adapting optimal transport to GANs. This makes a lot of sense. The paper makes some very good connections to the state of the art and those competing approaches. The proposal makes sense from the generative standpoint and it is clear from the paper that the key contribution is the design of the transport cost. I have two main remarks and questions.
* Regarding the transport cost, the authors say that the Euclidean distance does not work well. Did they try to use normalised vectors with the squared Euclidean distance ? I am asking this question because solving the OT problem with cost defined as in c_eta is equivalent to using a *normalized squared* Euclidean distance in the feature space defined by v_eta. If the answer is yes and it did not work, then there is indeed a real contribution to using the DNN. Otherwise, the contribution has to be balanced. In either case, I would have been happy to see numbers for comparison.
* The square mini batch energy distance looks very much like a maximum mean discrepancy criterion (see the work of A. Gretton), up to the sign, and also to regularised approached to MMD optimisation (see the paper of Kim, NIPS'16 and references therein). The MMD is the solution of an optimisation problem which, I suppose, has lots of connections with the dual Wasserstein GAN. The authors should elaborate on the relationships, and eventually discuss regularisation in this context.