Dualing GANs
Generative adversarial nets (GANs) are a promising technique for modeling a distribution from samples. It is however well known that GAN training suffers from instability due to the nature of its saddle point formulation. In this paper, we explore ways to tackle the instability problem by dualizing the discriminator. We start from linear discriminators in which case conjugate duality provides a mechanism to reformulate the saddle point objective into a maximization problem, such that both the generator and the discriminator of this 'dualing GAN' act in concert. We then demonstrate how to extend this intuition to non-linear formulations. For GANs with linear discriminators our approach is able to remove the instability in training, while for GANs with nonlinear discriminators our approach provides an alternative to the commonly used GAN training algorithm.
This submission proposes an alternative view on GAN training by replacing the inner learning of the discriminator by its dual program. In the case of linear discriminators this leads to a stable and simpler maximization problem. The authors propose strategies to cope with non-linear discriminators, by either taking linear approximations to the cost function, or to the scoring function (typically the CNN in the case of image GANs). 
PROS:
- The paper proposes an alternative and simple view on GAN training.
- The paper reads well and the formalism is well chosen.
- The proposed algorithm (with scoring function linearization) leads to interesting initial results on CIFAR and MNIST.
CONS:
- The proposed approach requires defining a dual variable for each sample z_i. Therefore, the dual program needs to be solved to satisfactory precision at each step. 
- If I am not mistaken, Claim 1 is simply the dual of a binary logistic linear classification problem. Then, it might be good to present it that way, and avoid calling that a "claim" as this is a classical result. 
- From a purely formatting point of view, the graphical presentation of results could be improved, as it is hard to read. Moreover, only several runs, and the corresponding learning curves are given. Would it be possible to give other quantitative measures? How often does GAN training diverge? Is the proposed algorithm helping that metric?
Overall, I think that this paper gives a simple view on GAN training using the dual of the inner problem. I enjoyed reading the paper and both the formal and experimental results seem correct. Because of this I lean towards acceptance - however, since I am not a pure GAN expert, I may have misevaluated the importance of this work.