Joint control variate for faster black-box variational inference

TL;DR

This paper introduces a joint control variate technique that simultaneously reduces variance from data subsampling and Monte Carlo sampling in black-box variational inference, resulting in faster convergence.

Contribution

The paper proposes a novel joint control variate method that addresses both sources of variance in gradient estimators, improving inference efficiency.

Findings

Significant variance reduction in gradient estimates.

Faster convergence in variational inference tasks.

Enhanced performance over existing variance reduction methods.

Abstract

Black-box variational inference performance is sometimes hindered by the use of gradient estimators with high variance. This variance comes from two sources of randomness: Data subsampling and Monte Carlo sampling. While existing control variates only address Monte Carlo noise, and incremental gradient methods typically only address data subsampling, we propose a new "joint" control variate that jointly reduces variance from both sources of noise. This significantly reduces gradient variance, leading to faster optimization in several applications.