  Generative adversarial networks (GANs) are a learning framework that rely on
training a discriminator to estimate a measure of difference between a target
and generated distributions. GANs, as normally formulated, rely on the
generated samples being completely differentiable w.r.t. the generative
parameters, and thus do not work for discrete data. We introduce a method for
training GANs with discrete data that uses the estimated difference measure
from the discriminator to compute importance weights for generated samples,
thus providing a policy gradient for training the generator. The importance
weights have a strong connection to the decision boundary of the discriminator,
and we call our method boundary-seeking GANs (BGANs). We demonstrate the
effectiveness of the proposed algorithm with discrete image and character-based
natural language generation. In addition, the boundary-seeking objective
extends to continuous data, which can be used to improve stability of training,
and we demonstrate this on Celeba, Large-scale Scene Understanding (LSUN)
bedrooms, and Imagenet without conditioning.
