Using Large Ensembles of Control Variates for Variational Inference

TL;DR

This paper introduces a systematic framework for combining large ensembles of control variates to significantly improve the convergence of variational inference by reducing gradient variance.

Contribution

It provides a Bayesian risk minimization approach for optimally combining control variates, enhancing convergence in stochastic variational inference.

Findings

Combining many control variates improves convergence rates.

The proposed method outperforms traditional gradient estimators.

A simple combination rule is effective for variance reduction.

Abstract

Variational inference is increasingly being addressed with stochastic optimization. In this setting, the gradient's variance plays a crucial role in the optimization procedure, since high variance gradients lead to poor convergence. A popular approach used to reduce gradient's variance involves the use of control variates. Despite the good results obtained, control variates developed for variational inference are typically looked at in isolation. In this paper we clarify the large number of control variates that are available by giving a systematic view of how they are derived. We also present a Bayesian risk minimization framework in which the quality of a procedure for combining control variates is quantified by its effect on optimization convergence rates, which leads to a very simple combination rule. Results show that combining a large number of control variates this way significantly improves the convergence of inference over using the typical gradient estimators or a reduced number of control variates.