Perturbation analysis via coupling

Abstract

Perturbation analysis is an efficient method for performance analysis of discrete event dynamic systems. It yields gradient information from only one sample path observation. Over the last two decades, various perturbation analysis techniques have been developed to handle a large class of problems. Coupling is a method of generating multiple random samples. It has wide range of applications in applied probability. The paper is concerned with perturbation analysis via coupling. This approach offers a great versatility of the form of gradient estimators, which is potentially useful for variance reduction and for efficient implementation. Several known perturbation analysis techniques can be reviewed as special ways of coupling. The coupling method is further applied to gradient estimation of Markov chains. The method is used not only in deriving a gradient estimator but also in its implementation. It is proved that the estimator is strongly consistent. Finally, different coupling schemes are compared using an illustrative example.