  Learning in models with discrete latent variables is challenging due to high
variance gradient estimators. Generally, approaches have relied on control
variates to reduce the variance of the REINFORCE estimator. Recent work (Jang
et al. 2016, Maddison et al. 2016) has taken a different approach, introducing
a continuous relaxation of discrete variables to produce low-variance, but
biased, gradient estimates. In this work, we combine the two approaches through
a novel control variate that produces low-variance, \emph{unbiased} gradient
estimates. Then, we introduce a modification to the continuous relaxation and
show that the tightness of the relaxation can be adapted online, removing it as
a hyperparameter. We show state-of-the-art variance reduction on several
benchmark generative modeling tasks, generally leading to faster convergence to
a better final log-likelihood.
