Dual control variate for faster black-box variational inference

Black-box variational inference is a widely-used framework for Bayesian posterior inference, but in some cases suffers from high variance in gradient estimates, harming accuracy and efficiency. This variance comes from two sources of randomness: Data subsampling and Monte Carlo sampling. Whereas existing control variates only address Monte Carlo noise and incremental gradient methods typically only address data subsampling, we propose a new "dual" control variate capable of jointly reducing variance from both sources of noise. We confirm that this leads to reduced variance and improved optimization in several real-world applications.