| 基于平均化的截尾随机逼近算法 |
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| 作者姓名： | 刘仁龙 杨建奎 熊世峰 |
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| 作者单位： | 1. 北京邮电大学理学院, 北京 100876;
2. 中国科学院数学与系统科学研究院, 北京 100190 |
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| 基金项目： | 国家自然科学基金(11271355,11101050,11471172)资助 |
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| 摘 要： | 考察带有随机干扰线性系统的随机逼近问题. 基于Polyak和Juditsky(SIAM J. Control & Optimization, 1992, 30:838-855)中的平均化加速算法,提出平均化的截尾算法. 证明该算法下随机逼近序列的强相合性和渐近正态性.
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| 关 键 词： | 渐近正态性 线性系统 强相合性 |
| 收稿时间： | 2014-04-16 |
| 修稿时间： | 2014-08-06 |
Averaging-based truncated stochastic approximation algorithm |
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| Authors: | LIU Renlong YANG Jiankui XIONG Shifeng |
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| Affiliation: | 1. School of Science, Beijing University of Posts and Telecommunications, Beijng 100876, China;
2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China |
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| Abstract: | In this work the stochastic approximation problem of perturbed linear systems was examined. Inspired by the averaging-based accelerated algorithm of Polyak and Juditsky(SIAM J. Control & Optimization,1992,30:838-855), we propose an averaging-based truncated algorithm. The almost sure convergence and asymptotic normality of the sequence defined by this algorithm are proved. |
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| Keywords: | asymptotic normality linear system strong consistency |
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