# Scalable Control Variates for Monte Carlo Methods via Stochastic Optimization

arXiv: https://arxiv.org/abs/2006.07487 · HTML: https://mlsanity.com/paper/2006.07487/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2020.

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

- [Gradient Estimation with Discrete Stein Operators](https://mlsanity.com/paper/2202.09497/) (2022)
- [A Dictionary of Closed-Form Kernel Mean Embeddings](https://mlsanity.com/paper/2504.18830/) (2025)
- [Meta-learning Control Variates: Variance Reduction with Limited Data](https://mlsanity.com/paper/2303.04756/) (2023)
- [Nested Expectations with Kernel Quadrature](https://mlsanity.com/paper/2502.18284/) (2025)
- [Variance Reduction for Policy-Gradient Methods via Empirical Variance Minimization](https://mlsanity.com/paper/2206.06827/) (2022)
- [Theoretical guarantees for neural control variates in MCMC](https://mlsanity.com/paper/2304.01111/) (2023)
- [Bayesian Numerical Integration with Neural Networks](https://mlsanity.com/paper/2305.13248/) (2023)
- [Conditional neural control variates for variance reduction in Bayesian inverse problems](https://mlsanity.com/paper/2602.21357/) (2026)
- [Training neural control variates using correlated configurations](https://mlsanity.com/paper/2505.07719/) (2025)
- [Pathwise Gradient Variance Reduction with Control Variates in Variational Inference](https://mlsanity.com/paper/2410.05753/) (2024)

## Abstract (arXiv)

Control variates are a well-established tool to reduce the variance of Monte Carlo estimators. However, for large-scale problems including high-dimensional and large-sample settings, their advantages can be outweighed by a substantial computational cost. This paper considers control variates based on Stein operators, presenting a framework that encompasses and generalizes existing approaches that use polynomials, kernels and neural networks. A learning strategy based on minimising a variational objective through stochastic optimization is proposed, leading to scalable and effective control variates. Novel theoretical results are presented to provide insight into the variance reduction that can be achieved, and an empirical assessment, including applications to Bayesian inference, is provided in support.