Title: KGAN: How to Break The Minimax Game in GAN,
Abstract: Generative Adversarial Networks (GANs) were intuitively and attractively
explained under the perspective of game theory, wherein two involving parties
are a discriminator and a generator. In this game, the task of the
discriminator is to discriminate the real and generated (i.e., fake) data,
whilst the task of the generator is to generate the fake data that maximally
confuses the discriminator. In this paper, we propose a new viewpoint for GANs,
which is termed as the minimizing general loss viewpoint. This viewpoint shows
a connection between the general loss of a classification problem regarding a
convex loss function and a f-divergence between the true and fake data
distributions. Mathematically, we proposed a setting for the classification
problem of the true and fake data, wherein we can prove that the general loss
of this classification problem is exactly the negative f-divergence for a
certain convex function f. This allows us to interpret the problem of learning
the generator for dismissing the f-divergence between the true and fake data
distributions as that of maximizing the general loss which is equivalent to the
min-max problem in GAN if the Logistic loss is used in the classification
problem. However, this viewpoint strengthens GANs in two ways. First, it allows
us to employ any convex loss function for the discriminator. Second, it
suggests that rather than limiting ourselves in NN-based discriminators, we can
alternatively utilize other powerful families. Bearing this viewpoint, we then
propose using the kernel-based family for discriminators. This family has two
appealing features: i) a powerful capacity in classifying non-linear nature
data and ii) being convex in the feature space. Using the convexity of this
family, we can further develop Fenchel duality to equivalently transform the
max-min problem to the max-max dual problem.