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首页> 外文期刊>SIAM Journal on Control and Optimization >A GENERALIZATION OF THE AVERAGING PROCEDURE: THE USE OF TWO-TIME-SCALE ALGORITHMS
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A GENERALIZATION OF THE AVERAGING PROCEDURE: THE USE OF TWO-TIME-SCALE ALGORITHMS

机译:平均过程的广义化:两次时间算法的使用

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Ruppert [Handbook of Sequential Analysis, B. K. Ghosh and P. K. Sen, eds., Marcel Dekker, New York, 1991] and Polyak [Automat. Remote Control, 51 (1990), pp. 937-946] independently introduced the averaging principle for Robbins-Monro's algorithm in order to construct an algorithm that is asymptotically efficient, and that is quickly updated. Their averaging principle has been extended to other algorithms (including Kiefer-Wolfowitz's algorithm), leading to algorithms that are asymptotically efficient, but whose updatings are less straightforward. We introduce the use of two-time-scale stochastic approximation algorithms to construct a large class of asymptotically efficient algorithms. This method generalizes the averaging principle. Moreover, for the algorithms that do not behave as Robbins-Monro's algorithm, it allows one to provide algorithms whose updating is as straightforward as that of the averaged Robbins-Monro's algorithm.
机译:Ruppert [顺序分析手册,B。K. Ghosh和P. K. Sen编辑,1991年,纽约,Marcel Dekker]和Polyak [自动机。 [Remote Control,51(1990),pp。937-946]独立介绍了Robbins-Monro算法的平均原理,以构造一种渐近有效且可快速更新的算法。它们的平均原理已扩展到其他算法(包括Kiefer-Wolfowitz的算法),导致渐近有效的算法,但更新不那么直接。我们介绍了使用二次尺度随机逼近算法来构造一大类渐近有效算法。该方法概括了平均原理。而且,对于不像Robbins-Monro算法那样工作的算法,它允许人们提供其更新与平均Robbins-Monro算法一样简单的算法。

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