Unbiased estimates for gradients of stochastic network performance measures

TL;DR

This paper develops general conditions and practical algorithms for obtaining unbiased gradient estimates of performance measures in stochastic networks, facilitating more accurate simulation-based optimization.

Contribution

It introduces broad, applicable conditions for unbiased gradient estimation and presents practical algorithms for their computation in stochastic network analysis.

Findings

Provided sufficient conditions for unbiased gradient estimates.

Developed practical algorithms for unbiased gradient calculation.

Applicable to various classes of stochastic networks.

Abstract

Three classes of stochastic networks and their performance measures are considered. These performance measures are defined as the expected value of some random variables and cannot normally be obtained analytically as functions of network parameters in a closed form. We give similar representations for the random variables to provide a useful way of analytical study of these functions and their gradients. The representations are used to obtain sufficient conditions for the gradient estimates to be unbiased. The conditions are rather general and usually met in simulation study of the stochastic networks. Applications of the results are discussed and some practical algorithms of calculating unbiased estimates of the gradients are also presented.