  This paper proposes Differential-Critic Generative Adversarial Network
(DiCGAN) to learn the distribution of user-desired data when only partial
instead of the entire dataset possesses the desired property. DiCGAN generates
desired data that meets the user's expectations and can assist in designing
biological products with desired properties. Existing approaches select the
desired samples first and train regular GANs on the selected samples to derive
the user-desired data distribution. However, the selection of the desired data
relies on global knowledge and supervision over the entire dataset. DiCGAN
introduces a differential critic that learns from pairwise preferences, which
are local knowledge and can be defined on a part of training data. The critic
is built by defining an additional ranking loss over the Wasserstein GAN's
critic. It endows the difference of critic values between each pair of samples
with the user preference and guides the generation of the desired data instead
of the whole data. For a more efficient solution to ensure data quality, we
further reformulate DiCGAN as a constrained optimization problem, based on
which we theoretically prove the convergence of our DiCGAN. Extensive
experiments on a diverse set of datasets with various applications demonstrate
that our DiCGAN achieves state-of-the-art performance in learning the
user-desired data distributions, especially in the cases of insufficient
desired data and limited supervision.
