ACHIEVING OPTIMAL BIAS-VARIANCE TRADEOFF IN ONLINE DERIVATIVE ESTIMATION

The finite-difference method has been commonly used in stochastic derivative estimation when an unbiased derivative estimator is unavailable or costly. The efficiency of this method relies on the choice of a perturbation parameter, which needs to be calibrated based on the number of simulation replications. We study the setting where such an a priori planning of simulation runs is difficult, which could arise due to the variability of runtime for complex simulation models or interruptions. We show how a simple recursive weighting scheme on simulation outputs can recover, in an online fashion, the optimal asymptotic bias-variance tradeoff achieved by the conventional scheme where the replication size is known in advance.