  Stochastic gradient-based optimisation for discrete latent variable models is
challenging due to the high variance of gradients. We introduce a variance
reduction technique for score function estimators that makes use of double
control variates. These control variates act on top of a main control variate,
and try to further reduce the variance of the overall estimator. We develop a
double control variate for the REINFORCE leave-one-out estimator using Taylor
expansions. For training discrete latent variable models, such as variational
autoencoders with binary latent variables, our approach adds no extra
computational cost compared to standard training with the REINFORCE
leave-one-out estimator. We apply our method to challenging high-dimensional
toy examples and training variational autoencoders with binary latent
variables. We show that our estimator can have lower variance compared to other
state-of-the-art estimators.
