  Recently, we and several other authors have written about the possibilities
of using stochastic approximation techniques for fitting variational
approximations to intractable Bayesian posterior distributions. Naive
implementations of stochastic approximation suffer from high variance in this
setting. Several authors have therefore suggested using control variates to
reduce this variance, while we have taken a different but analogous approach to
reducing the variance which we call stochastic linear regression. In this note
we take the former perspective and derive the ideal set of control variates for
stochastic approximation variational Bayes under a certain set of assumptions.
We then show that using these control variates is closely related to using the
stochastic linear regression approximation technique we proposed earlier. A
simple example shows that our method for constructing control variates leads to
stochastic estimators with much lower variance compared to other approaches.
