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Stochastic approximation (SA) algorithms are widely used in systemoptimization problems when only noisy measurements of the system are available.This paper studies two types of SA algorithms in a multivariateKiefer-Wolfowitz setting: random-direction SA (RDSA) andsimultaneous-perturbation SA (SPSA), and then describes the bias term,convergence, and asymptotic normality of RDSA algorithms. The gradientestimations in RDSA and SPSA have different forms and, consequently, usedifferent types of random perturbations. This paper looks at various validdistributions for perturbations in RDSA and SPSA and then compares the twoalgorithms using mean-square errors computed from asymptotic distribution. Fromboth a theoretical and numerical point of view, we find that SPSA generallyoutperforms RDSA.

Theoretical Study and Comparison of SPSA and RDSA Algorithms