# Approximation Based Variance Reduction for Reparameterization Gradients

arXiv: https://arxiv.org/abs/2007.14634 · HTML: https://mlsanity.com/paper/2007.14634/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2020.

## Built on by (most cited first, 10 of 10)

- [Provable convergence guarantees for black-box variational inference](https://mlsanity.com/paper/2306.03638/) (2023)
- [Probabilistic Mixture-of-Experts for Efficient Deep Reinforcement Learning](https://mlsanity.com/paper/2104.09122/) (2021)
- [Generalized Doubly Reparameterized Gradient Estimators](https://mlsanity.com/paper/2101.11046/) (2021)
- [Linear Convergence of Black-Box Variational Inference: Should We Stick the Landing?](https://mlsanity.com/paper/2307.14642/) (2023)
- [U-Statistics for Importance-Weighted Variational Inference](https://mlsanity.com/paper/2302.13918/) (2023)
- [Nearly Dimension-Independent Convergence of Mean-Field Black-Box Variational Inference](https://mlsanity.com/paper/2505.21721/) (2025)
- [Scalable Mean-Field Variational Inference via Preconditioned Primal-Dual Optimization](https://mlsanity.com/paper/2602.07632/) (2026)
- [Joint control variate for faster black-box variational inference](https://mlsanity.com/paper/2210.07290/) (2022)
- [Pathwise Gradient Variance Reduction with Control Variates in Variational Inference](https://mlsanity.com/paper/2410.05753/) (2024)
- [Stochastic Gradient Variational Inference with Price's Gradient Estimator from Bures-Wasserstein to Parameter Space](https://mlsanity.com/paper/2602.18718/) (2026)

## Abstract (arXiv)

Flexible variational distributions improve variational inference but are harder to optimize. In this work we present a control variate that is applicable for any reparameterizable distribution with known mean and covariance matrix, e.g. Gaussians with any covariance structure. The control variate is based on a quadratic approximation of the model, and its parameters are set using a double-descent scheme by minimizing the gradient estimator's variance. We empirically show that this control variate leads to large improvements in gradient variance and optimization convergence for inference with non-factorized variational distributions.