Provable Gradient Variance Guarantees for Black-Box Variational Inference
This work addresses a theoretical gap for researchers in variational inference, offering foundational guarantees that are incremental but precise.
The paper tackles the problem of understanding variance in stochastic gradient estimators for black-box variational inference, providing unimprovable bounds for reparameterization estimators under smooth target and location-scale variational family assumptions.
Recent variational inference methods use stochastic gradient estimators whose variance is not well understood. Theoretical guarantees for these estimators are important to understand when these methods will or will not work. This paper gives bounds for the common "reparameterization" estimators when the target is smooth and the variational family is a location-scale distribution. These bounds are unimprovable and thus provide the best possible guarantees under the stated assumptions.