Minimax Efficient Finite-Difference Stochastic Gradient Estimators Using Black-Box Function Evaluations

07/08/2020

∙

by   Henry Lam, et al.

∙

0

∙

share

We consider stochastic gradient estimation using noisy black-box function evaluations. A standard approach is to use the finite-difference method or its variants. While natural, it is open to our knowledge whether its statistical accuracy is the best possible. This paper argues so by showing that central finite-difference is a nearly minimax optimal zeroth-order gradient estimator, among both the class of linear estimators and the much larger class of all (nonlinear) estimators.