Generalized Simultaneous Perturbation Stochastic Approximation with Reduced Estimator Bias

Abstract

We present in this paper a family of generalized simultaneous perturbation stochastic approximation (G-SPSA) estimators that estimate the gradient of the objective using noisy function measurements, but where the number of function measurements and the form of the gradient estimator is guided by the desired estimator bias. In particular, estimators with more function measurements are seen to result in lower bias. We provide an analysis of convergence of generalized SPSA, and point to possible future directions.