# Adaptively Optimised Adaptive Importance Samplers

arXiv: https://arxiv.org/abs/2307.09341 · HTML: https://mlsanity.com/paper/2307.09341/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 32 references that are in the map.
- First posted on arXiv 18 Jul 2023.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Simple Convergence Proof of Adam and Adagrad](https://mlsanity.com/paper/2003.02395/) (2020)
- [Layered Adaptive Importance Sampling](https://mlsanity.com/paper/1505.04732/) (2015)
- [Convergence rates for optimised adaptive importance samplers](https://mlsanity.com/paper/1903.12044/) (2019)
- [Adaptive Importance Sampling via Stochastic Convex Programming](https://mlsanity.com/paper/1412.4845/) (2014)
- [Global convergence of optimized adaptive importance samplers](https://mlsanity.com/paper/2201.00409/) (2022)
- [Hamiltonian Adaptive Importance Sampling](https://mlsanity.com/paper/2209.13716/) (2022)

## Built on by (most cited first, 1 of 1)

- [Amortised adaptive importance sampling](https://mlsanity.com/paper/2610.16736/) (2026)

## Abstract (arXiv)

We introduce a new class of adaptive importance samplers leveraging adaptive optimisation tools, which we term AdaOAIS. We build on Optimised Adaptive Importance Samplers (OAIS), a class of techniques that adapt proposals to improve the mean-squared error of the importance sampling estimators by parameterising the proposal and optimising the chi2-divergence between the target and the proposal. We show that a naive implementation of OAIS using stochastic gradient descent may lead to unstable estimators despite its convergence guarantees. To remedy this shortcoming, we instead propose to use adaptive optimisers (such as AdaGrad and Adam) to improve the stability of the OAIS. We provide convergence results for AdaOAIS in a similar manner to OAIS. We also provide empirical demonstration on a variety of examples and show that AdaOAIS lead to stable importance sampling estimators in practice.