论文标题
总体化同时基于扰动的梯度搜索，估计器偏差减少
Generalized Simultaneous Perturbation-based Gradient Search with Reduced Estimator Bias
论文作者
论文摘要
我们在本文中介绍了使用噪声函数测量值的一系列广义同时基于扰动的梯度搜索（GSPGS）估计器。每个估计器所需的功能测量数量以所需的准确性水平为指导。我们首先详细介绍了不平衡的广义同时扰动随机近似（GSPSA）估计量，后来介绍了这些估计值的平衡版本（B-GSPSA）。我们进一步扩展了这个想法，并介绍了广义平滑功能（GSF）和广义随机方向随机近似（GRDSA）估计量及其平衡变体。我们显示，需要更多功能测量的任何指定类中的估计器会导致估计值偏差较低。我们介绍了所得随机近似方案的渐近和非反应收敛性的详细分析。我们进一步提出了一系列实验结果，其中包括rastrigin和二次功能目标的各种GSPGS估计量。我们可以看到我们的实验来验证我们的理论发现。
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.
