To backpropagate the gradients through stochastic binary layers, we propose the augment-REINFORCE-merge (ARM) estimator that is unbiased, exhibits low variance, and has low computational complexity. Exploiting variable augmentation, REINFORCE, and reparameterization, the ARM estimator achieves adaptive variance reduction for Monte Carlo integration by merging two expectations via common random numbers. The variance-reduction mechanism of the ARM estimator can also be attributed to either antithetic sampling in an augmented space, or the use of an optimal anti-symmetric "self-control" baseline function together with the REINFORCE estimator in that augmented space. Experimental results show the ARM estimator provides state-of-the-art performance in auto-encoding variational inference and maximum likelihood estimation, for discrete latent variable models with one or multiple stochastic binary layers. Python code for reproducible research is publicly available.
An unbiased and low-variance gradient estimator for discrete latent variable models Proposes a new variance-reduction technique to use when computing an expected loss gradient where the expectation is with respect to independent binary random variables. An algorithm combining Rao-Blackwellization and common random numbers for lowering the variance of the score-function gradient estimator in the special case of stochastic binary networks An unbiased and low variance augment-REINFORCE-merge (ARM) estimator for calculating and backpropagating gradients in binary neural networks