# Provable convergence guarantees for black-box variational inference

**Authors:** Justin Domke, Guillaume Garrigos, Robert Gower  
**arXiv:** [2306.03638](https://arxiv.org/abs/2306.03638)  
**Date:** 2023-06-04  
**Summary page:** https://www.summarizepaper.com/fr/paper/2306.03638v1/

## Abstract

While black-box variational inference is widely used, there is no proof that its stochastic optimization succeeds. We suggest this is due to a theoretical gap in existing stochastic optimization proofs-namely the challenge of gradient estimators with unusual noise bounds, and a composite non-smooth objective. For dense Gaussian variational families, we observe that existing gradient estimators based on reparameterization satisfy a quadratic noise bound and give novel convergence guarantees for proximal and projected stochastic gradient descent using this bound. This provides the first rigorous guarantee that black-box variational inference converges for realistic inference problems.