  In standard generative adversarial network (SGAN), the discriminator
estimates the probability that the input data is real. The generator is trained
to increase the probability that fake data is real. We argue that it should
also simultaneously decrease the probability that real data is real because 1)
this would account for a priori knowledge that half of the data in the
mini-batch is fake, 2) this would be observed with divergence minimization, and
3) in optimal settings, SGAN would be equivalent to integral probability metric
(IPM) GANs.
  We show that this property can be induced by using a relativistic
discriminator which estimate the probability that the given real data is more
realistic than a randomly sampled fake data. We also present a variant in which
the discriminator estimate the probability that the given real data is more
realistic than fake data, on average. We generalize both approaches to
non-standard GAN loss functions and we refer to them respectively as
Relativistic GANs (RGANs) and Relativistic average GANs (RaGANs). We show that
IPM-based GANs are a subset of RGANs which use the identity function.
  Empirically, we observe that 1) RGANs and RaGANs are significantly more
stable and generate higher quality data samples than their non-relativistic
counterparts, 2) Standard RaGAN with gradient penalty generate data of better
quality than WGAN-GP while only requiring a single discriminator update per
generator update (reducing the time taken for reaching the state-of-the-art by
400%), and 3) RaGANs are able to generate plausible high resolutions images
(256x256) from a very small sample (N=2011), while GAN and LSGAN cannot; these
images are of significantly better quality than the ones generated by WGAN-GP
and SGAN with spectral normalization.
