Stochastic approximation (SA) algorithms are widely 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 describes the bias term, convergence, and asymptotic normality of RDSA algorithms. The gradient estimations in RDSA and SPSA have different forms and, consequently, use different types of random perturbations. This paper looks at various valid distributions for perturbations in RDSA and SPSA and then compares the two algorithms using mean-square errors computed from asymptotic distribution. From both a theoretical and numerical point of view, we find that SPSA generally outperforms RDSA.

翻译：在系统优化问题中,只有对系统进行吵闹的测量,才广泛使用沙粒近似算法(SA),本文研究多种变式基费尔-沃福威茨设置的两种SA算法:随机方向SA(RDSA)和同时扰动SA(SPSA),然后描述RDSA算法的偏差术语、趋同和无症状常态。RDSA和SPSA的梯度估计有不同的形式,因此使用不同类型的随机扰动。本文考察了RDSA和SPSA中各种有效的扰动分布,然后比较了使用从无症状分布中计算出的平均平方差差的两种算法。从理论和数字的角度来看,我们发现SPSA一般都比RDSA高。