Using Importance Samping in Estimating Weak Derivative

TL;DR

This paper introduces a new importance sampling-based method for estimating weak derivatives in stochastic networks, reducing computational cost and variance, and providing more precise gradient estimates in simulations.

Contribution

The paper presents a novel importance sampling transform for weak derivative estimation that is computationally more efficient and maintains low variance, improving upon classical methods.

Findings

The new method reduces computational cost compared to classical approaches.

It does not significantly increase estimator variance in queueing and activity networks.

Numerical results show narrower confidence intervals for gradients using the new method.

Abstract

In this paper we study simulation-based methods for estimating gradients in stochastic networks. We derive a new method of calculating weak derivative estimator using importance sampling transform, and our method has less computational cost than the classical method. In the context of M/M/1 queueing network and stochastic activity network, we analytically show that our new method won't result in a great increase of sample variance of the estimators. Our numerical experiments show that under same simulation time, the new method can yield a narrower confidence interval of the true gradient than the classical one, suggesting that the new method is more competitive.