Convergence Rates of Finite-Difference Sensitivity Estimates for Stochastic Systems

A mean square error analysis of finite-difference sensitivity estimators for stochastic systems is presented and an expression for the optimal size of the increment is derived. The asymptotic behavior of the optimal increments, and the behavior of the corresponding optimal finite-difference (FD) estimators are investigated for finite-horizon experiments. Steady-state estimation is also considered for regenerative systems and in this context a convergence analysis of ratio estimators is presented. The use of variance reduction techniques for these FD estimates, such as common random numbers in simulation experiments, is not considered here. In the case here, direct gradient estimation techniques (such as perturbation analysis and likelihood ratio methods) whenever applicable, are shown to converge asymptotically faster than the optimal FD estimators.