Comparison of RDSA and SPSA algorithms with different perturbations

Stochastic approximation (SA) algorithms can be used in system optimization problems when only noisy measurements of the system are available. This paper studies two types of SA algorithms in a multivariate Kiefer-Wolfowitz setting: random-direction SA (RDSA) and simultaneous-perturbation SA (SPSA), and then presents a complete proof for the convergence and asymptotic normality of the RDSA algorithm. Finally, this paper looks at several valid distributed perturbations in RDSA and SPSA and compares the two algorithms using mean-square errors in both theoretical and numerical ways.