Discrete simultaneous perturbation stochastic approximation on loss function with noisy measurements

Consider the stochastic optimization of a loss function defined on p-dimensional grid of points in Euclidean space. We introduce the middle point discrete simultaneous perturbation stochastic approximation (DSPSA) algorithm for such discrete problems and show that convergence to the minimum is achieved. Consistent with other stochastic approximation methods, this method formally accommodates noisy measurements of the loss function.