Adaptively Optimised Adaptive Importance Samplers

TL;DR

This paper introduces AdaOAIS, an adaptive importance sampling method that uses adaptive optimization algorithms like AdaGrad and Adam to enhance stability and convergence, demonstrated through empirical results.

Contribution

It proposes a novel adaptive importance sampler leveraging adaptive optimizers to improve stability and convergence over traditional OAIS methods.

Findings

AdaOAIS achieves stable importance sampling estimators in practice.

Convergence results for AdaOAIS are established similar to OAIS.

Empirical examples demonstrate improved stability of importance sampling estimators.

Abstract

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 $\chi^2$-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.