Stochastic gradient estimation using a single design point

Using concepts arising in control variates, we propose estimating gradients using Monte Carlo data from a single design point. Our goal is to create a statistically efficient estimator that is easy to implement, with no analysis within the simulation oracle and no unknown algorithm parameters. We compare a simple version of the proposed method to finite differences and simultaneous perturbation, assuming first and second-order linear logic models and response surfaces. Results of the analysis indicate that the proposed gradient estimator is unbiased with variance that is inversely related to the variance of the assumed input model. Compared to the only existing single design-point method, the proposed gradient estimator is advantageous in that its variance is not dependent on the magnitude of the response surface at the design point of interest and also decreases as the simulation run length increases.