We present in this paper a family of generalized simultaneous perturbation-based gradient search (GSPGS) estimators that use noisy function measurements. The number of function measurements required by each estimator is guided by the desired level of accuracy. We first present in detail unbalanced generalized simultaneous perturbation stochastic approximation (GSPSA) estimators and later present the balanced versions (B-GSPSA) of these. We extend this idea further and present the generalized smoothed functional (GSF) and generalized random directions stochastic approximation (GRDSA) estimators, respectively, as well as their balanced variants. We show that estimators within any specified class requiring more number of function measurements result in lower estimator bias. We present a detailed analysis of both the asymptotic and non-asymptotic convergence of the resulting stochastic approximation schemes. We further present a series of experimental results with the various GSPGS estimators on the Rastrigin and quadratic function objectives. Our experiments are seen to validate our theoretical findings.

翻译：摘要：本文提出了一类基于广义同步扰动的梯度搜索（GSPGS）估计器，这些估计器利用含噪函数测量值，每个估计器所需的函数测量次数由其期望精度决定。我们首先详细介绍了非平衡广义同步扰动随机逼近（GSPSA）估计器，随后给出其平衡版本（B-GSPSA）。在此基础上进一步推广，分别提出广义平滑泛函（GSF）估计器、广义随机方向随机逼近（GRDSA）估计器及其平衡变体。研究表明，在特定估计器族中，需要更多函数测量次数的估计器能有效降低估计偏差。我们详细分析了由此产生的随机逼近方案的渐近与非渐近收敛性。最后，我们在Rastrigin函数和二次函数目标上对各类GSPGS估计器进行了系列实验，实验结果验证了理论发现。