Double Control Variates for Gradient Estimation in Discrete Latent Variable Models

Michalis Titsias, Jiaxin Shi

Keywords: Gradient estimation, Monte Carlo, score function, REINFORCE, discrete latent variables, VAE, latent variable models, control variates, variance reduction

TL;DR: A control variate for the REINFORCE leave-one-out gradient estimator without extra function evaluations.

Abstract: 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.