Adaptive Importance Sampling via Stochastic Convex Programming
Methodology
2015-01-12 v2 Optimization and Control
Computation
Abstract
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.
Cite
@article{arxiv.1412.4845,
title = {Adaptive Importance Sampling via Stochastic Convex Programming},
author = {Ernest K. Ryu and Stephen P. Boyd},
journal= {arXiv preprint arXiv:1412.4845},
year = {2015}
}