Stochastic gradient estimation using a single design point

We propose and analyze a black-box gradient estimation method that can estimate gradients with respect to multiple input parameters using data obtained from a single design point. We identify conditions under which the proposed estimator is unbiased and converges in mean squared error. The proposed method is applicable to problems where the input parameter can be estimated. We compare the proposed method to finite differences and simultaneous perturbation. Relative to these methods, the proposed method is advantageous in that it yields a gradient estimate with no additional computational effort when batching methods or multiple replications are used to obtain a point estimator for the performance measure of interest. Another advantage of the proposed method is that it requires users to specify batch size, rather than input-parameter perturbations, which can be changed and adjusted after the experiment has been completed. Finite differences and simultaneous perturbation require users to specify input-parameter perturbations, which cannot be changed once the data have been collected. The proposed method outperforms existing methods in most cases when implemented on an M/M/C queuing model with random assignment of customers to individual queues. In general, however, the preferred method is problem specific. Numerical results illustrate that the performance of the proposed method is dependent on the batch size. The proposed gradient estimation method is especially efficient when the input parameters are uncorrelated because there is no loss of degrees of freedom for estimating gradients with respect to additional uncorrelated parameters