# Optimal Variance Control of the Score Function Gradient Estimator for Importance Weighted Bounds

arXiv: https://arxiv.org/abs/2008.01998 · HTML: https://mlsanity.com/paper/2008.01998/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2020.

## Built on by (most cited first, 7 of 7)

- [Variational Open-Domain Question Answering](https://mlsanity.com/paper/2210.06345/) (2022)
- [Uphill Roads to Variational Tightness: Monotonicity and Monte Carlo Objectives](https://mlsanity.com/paper/2201.10989/) (2022)
- [U-Statistics for Importance-Weighted Variational Inference](https://mlsanity.com/paper/2302.13918/) (2023)
- [Joint Causal Structure and Cluster Discovery Using Variational Inference](https://mlsanity.com/paper/2608.22212/) (2026)
- [Stochastic automatic differentiation for Monte Carlo processes](https://mlsanity.com/paper/2307.15406/) (2023)
- [A Generative Sampler for distributions with possible discrete parameter based on Reversibility](https://mlsanity.com/paper/2603.09251/) (2026)
- [Weave of Formal Thought](https://mlsanity.com/paper/2606.25987/) (2026)

## Abstract (arXiv)

This paper introduces novel results for the score function gradient estimator of the importance weighted variational bound (IWAE). We prove that in the limit of large K (number of importance samples) one can choose the control variate such that the Signal-to-Noise ratio (SNR) of the estimator grows as √K. This is in contrast to the standard pathwise gradient estimator where the SNR decreases as 1/√K. Based on our theoretical findings we develop a novel control variate that extends on VIMCO. Empirically, for the training of both continuous and discrete generative models, the proposed method yields superior variance reduction, resulting in an SNR for IWAE that increases with K without relying on the reparameterization trick. The novel estimator is competitive with state-of-the-art reparameterization-free gradient estimators such as Reweighted Wake-Sleep (RWS) and the thermodynamic variational objective (TVO) when training generative models.