  Generative Adversarial Networks (GANs) have emerged as useful generative
models, which are capable of implicitly learning data distributions of
arbitrarily complex dimensions. However, the training of GANs is empirically
well-known for being highly unstable and sensitive. The loss functions of both
the discriminator and generator concerning their parameters tend to oscillate
wildly during training. Different loss functions have been proposed to
stabilize the training and improve the quality of images generated. In this
paper, we perform an empirical study on the impact of several loss functions on
the performance of standard GAN models, Deep Convolutional Generative
Adversarial Networks (DCGANs). We introduce a new improvement that employs a
relativistic discriminator to replace the classical deterministic discriminator
in DCGANs and implement a margin cosine loss function for both the generator
and discriminator. This results in a novel loss function, namely Relativistic
Margin Cosine Loss (RMCosGAN). We carry out extensive experiments with four
datasets: CIFAR-$10$, MNIST, STL-$10$, and CAT. We compare RMCosGAN performance
with existing loss functions based on two metrics: Frechet inception distance
and inception score. The experimental results show that RMCosGAN outperforms
the existing ones and significantly improves the quality of images generated.
