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.

本文介绍了使用控制变量的方法来减少渐变方差的影响，提出了一种贝叶斯风险最小化框架来定量评估这一方法的效果，并表明使用大量控制变量结合的方法显著提高了推理的收敛性。

使用大量控制变量的集成进行变分推断