# Adaptive Importance Sampling via Stochastic Convex Programming

arXiv: https://arxiv.org/abs/1412.4845 · HTML: https://mlsanity.com/paper/1412.4845/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Dec 2014.

## Built on by (most cited first, 3 of 3)

- [Unrolling Particles: Unsupervised Learning of Sampling Distributions](https://mlsanity.com/paper/2110.02915/) (2021)
- [Global convergence of optimized adaptive importance samplers](https://mlsanity.com/paper/2201.00409/) (2022)
- [Adaptively Optimised Adaptive Importance Samplers](https://mlsanity.com/paper/2307.09341/) (2023)

## Abstract (arXiv)

We show that the variance of the Monte Carlo estimator that is importance sampled from an exponential family is a convex function of the natural parameter of the distribution. With this insight, we propose an adaptive importance sampling algorithm that simultaneously improves the choice of sampling distribution while accumulating a Monte Carlo estimate. Exploiting convexity, we prove that the method's unbiased estimator has variance that is asymptotically optimal over the exponential family.