Weighted Means in Stochastic Approximation of Minima
Weighted Means in Stochastic Approximation of Minima
复制标题
最小值随机逼近的加权平均值
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
J. Renz
中科院分区：
文献类型：
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作者：
Jürgen Dippon;J. Renz
加权平均的基弗-沃尔夫维茨型程序，这是由更大的步长比通常的驱动，可以达到最佳的收敛速度。避免了Hessian矩阵最小特征值下界的先验知识。加权平均算法的渐近均方误差与使用牛顿型自适应算法的渐近均方误差相同。考虑了几种不同的梯度估计;其中之一导致渐进偏差消失。与标准算法相比，加权平均算法应用的梯度估计通常产生更好的渐近均方误差。
Weighted averages of Kiefer--Wolfowitz-type procedures, which are driven by larger step lengths than usual, can achieve the optimal rate of convergence. A priori knowledge of a lower bound on the smallest eigenvalue of the Hessian matrix is avoided. The asymptotic mean squared error of the weighted averaging algorithm is the same as would emerge using a Newton-type adaptive algorithm. Several different gradient estimates are considered; one of them leads to a vanishing asymptotic bias. This gradient estimate applied with the weighted averaging algorithm usually yields a better asymptotic mean squared error than applied with the standard algorithm.