  Gradient estimation is often necessary for fitting generative models with
discrete latent variables, in contexts such as reinforcement learning and
variational autoencoder (VAE) training. The DisARM estimator (Yin et al. 2020;
Dong, Mnih, and Tucker 2020) achieves state of the art gradient variance for
Bernoulli latent variable models in many contexts. However, DisARM and other
estimators have potentially exploding variance near the boundary of the
parameter space, where solutions tend to lie. To ameliorate this issue, we
propose a new gradient estimator \textit{bitflip}-1 that has lower variance at
the boundaries of the parameter space. As bitflip-1 has complementary
properties to existing estimators, we introduce an aggregated estimator,
\textit{unbiased gradient variance clipping} (UGC) that uses either a bitflip-1
or a DisARM gradient update for each coordinate. We theoretically prove that
UGC has uniformly lower variance than DisARM. Empirically, we observe that UGC
achieves the optimal value of the optimization objectives in toy experiments,
discrete VAE training, and in a best subset selection problem.
