  Training generative adversarial networks (GAN) in a distributed fashion is a
promising technology since it is contributed to training GAN on a massive of
data efficiently in real-world applications. However, GAN is known to be
difficult to train by SGD-type methods (may fail to converge) and the
distributed SGD-type methods may also suffer from massive amount of
communication cost. In this paper, we propose a {distributed GANs training
algorithm with quantized gradient, dubbed DQGAN,} which is the first
distributed training method with quantized gradient for GANs. The new method
trains GANs based on a specific single machine algorithm called Optimistic
Mirror Descent (OMD) algorithm, and is applicable to any gradient compression
method that satisfies a general $\delta$-approximate compressor. The
error-feedback operation we designed is used to compensate for the bias caused
by the compression, and moreover, ensure the convergence of the new method.
Theoretically, we establish the non-asymptotic convergence of {DQGAN} algorithm
to first-order stationary point, which shows that the proposed algorithm can
achieve a linear speedup in the parameter server model. Empirically, our
experiments show that our {DQGAN} algorithm can reduce the communication cost
and save the training time with slight performance degradation on both
synthetic and real datasets.
