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Generative Adversarial Networks (GANs) were intuitively and attractivelyexplained under the perspective of game theory, wherein two involving partiesare a discriminator and a generator. In this game, the task of thediscriminator is to discriminate the real and generated (i.e., fake) data,whilst the task of the generator is to generate the fake data that maximallyconfuses the discriminator. In this paper, we propose a new viewpoint for GANs,which is termed as the minimizing general loss viewpoint. This viewpoint showsa connection between the general loss of a classification problem regarding aconvex loss function and a f-divergence between the true and fake datadistributions. Mathematically, we proposed a setting for the classificationproblem of the true and fake data, wherein we can prove that the general lossof this classification problem is exactly the negative f-divergence for acertain convex function f. This allows us to interpret the problem of learningthe generator for dismissing the f-divergence between the true and fake datadistributions as that of maximizing the general loss which is equivalent to themin-max problem in GAN if the Logistic loss is used in the classificationproblem. However, this viewpoint strengthens GANs in two ways. First, it allowsus to employ any convex loss function for the discriminator. Second, itsuggests that rather than limiting ourselves in NN-based discriminators, we canalternatively utilize other powerful families. Bearing this viewpoint, we thenpropose using the kernel-based family for discriminators. This family has twoappealing features: i) a powerful capacity in classifying non-linear naturedata and ii) being convex in the feature space. Using the convexity of thisfamily, we can further develop Fenchel duality to equivalently transform themax-min problem to the max-max dual problem.

KGAN: How to Break The Minimax Game in GAN