  Recent literature has demonstrated promising results for training Generative
Adversarial Networks by employing a set of discriminators, in contrast to the
traditional game involving one generator against a single adversary. Such
methods perform single-objective optimization on some simple consolidation of
the losses, e.g. an arithmetic average. In this work, we revisit the
multiple-discriminator setting by framing the simultaneous minimization of
losses provided by different models as a multi-objective optimization problem.
Specifically, we evaluate the performance of multiple gradient descent and the
hypervolume maximization algorithm on a number of different datasets. Moreover,
we argue that the previously proposed methods and hypervolume maximization can
all be seen as variations of multiple gradient descent in which the update
direction can be computed efficiently. Our results indicate that hypervolume
maximization presents a better compromise between sample quality and
computational cost than previous methods.
