Gradient Estimation with Discrete Stein Operators

TL;DR

This paper introduces a Stein operator-based variance reduction method for gradient estimation in discrete distributions, significantly improving the efficiency of training models like binary variational autoencoders.

Contribution

It develops a novel variance reduction technique using Stein operators for discrete distributions, enabling more accurate and efficient gradient estimates without extra function evaluations.

Findings

Achieves substantially lower variance than existing estimators.

Effective in training binary variational autoencoders.

Does not require additional target function evaluations.

Abstract

Gradient estimation -- approximating the gradient of an expectation with respect to the parameters of a distribution -- is central to the solution of many machine learning problems. However, when the distribution is discrete, most common gradient estimators suffer from excessive variance. To improve the quality of gradient estimation, we introduce a variance reduction technique based on Stein operators for discrete distributions. We then use this technique to build flexible control variates for the REINFORCE leave-one-out estimator. Our control variates can be adapted online to minimize variance and do not require extra evaluations of the target function. In benchmark generative modeling tasks such as training binary variational autoencoders, our gradient estimator achieves substantially lower variance than state-of-the-art estimators with the same number of function evaluations.