  Generative adversarial networks (GANs) have emerged as a powerful tool for
generating high-fidelity data. However, the main bottleneck of existing
approaches is the lack of supervision on the generator training, which often
results in undamped oscillation and unsatisfactory performance. To address this
issue, we propose an algorithm called Monte Carlo GAN (MCGAN). This approach,
utilizing an innovative generative loss function, termly the regression loss,
reformulates the generator training as a regression task and enables the
generator training by minimizing the mean squared error between the
discriminator's output of real data and the expected discriminator of fake
data. We demonstrate the desirable analytic properties of the regression loss,
including discriminability and optimality, and show that our method requires a
weaker condition on the discriminator for effective generator training. These
properties justify the strength of this approach to improve the training
stability while retaining the optimality of GAN by leveraging strong
supervision of the regression loss. Numerical results on CIFAR-10 and CIFAR-100
datasets demonstrate that the proposed MCGAN significantly and consistently
improves the existing state-of-the-art GAN models in terms of quality,
accuracy, training stability, and learned latent space. Furthermore, the
proposed algorithm exhibits great flexibility for integrating with a variety of
backbone models to generate spatial images, temporal time-series, and
spatio-temporal video data.
