Stochastic Approximation: A Dynamical Systems Viewpoint
Stochastic Approximation: A Dynamical Systems Viewpoint
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DOI：
10.1007/978-93-86279-38-5
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发表时间：
2008-09
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影响因子：
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通讯作者：
V. Borkar
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作者：
V. Borkar
随机逼近是在1951年的一篇文章中介绍的数学统计年鉴罗宾斯和门罗。最初被认为是统计计算的工具，在这个领域它保留了一个自豪的地方，它已经在一个完全不同的学科中蓬勃发展，即，那就是工程学。通信工程中的“自适应信号处理”的整个领域一直由随机近似算法和变体主导，即使粗略地看一下关于该主题的任何标准文本也可以看出这一点。然后有更多的最近的应用程序在通信网络中的自适应资源分配问题。在控制工程中，随机逼近也是系统辨识和自适应控制的在线算法的主要范例，这不是偶然的。在大多数这些应用中，关键词是自适应。随机近似有几个内在的特点，使其成为一个有吸引力的框架自适应计划。它是专为不确定的（读“随机”）环境，在那里它允许一个跟踪的“平均”或“典型”的行为，这样的环境。它是增量的，即，它在每一步都做一些小的改变，这确保了算法的优雅行为。这是任何自适应方案的非常期望的特征。此外，它通常具有较低的计算和存储器要求，每千兆比特，另一个理想的自适应系统的功能。最后，它符合我们拟人化的适应概念：它根据从环境中收到的反馈进行微小的调整，以提高一定的性能标准。
Stochastic approximation was introduced in a 1951 article in the Annals of Mathematical Statistics by Robbins and Monro. Originally conceived as a tool for statistical computation, an area in which it retains a place of pride, it has come to thrive in a totally different discipline, viz., that of engineering. The entire area of ‘adaptive signal processing’in communication engineering has been dominated by stochastic approximation algorithms and variants, as is evident from even a cursory look at any standard text on the subject. Then there are more recent applications to adaptive resource allocation problems in communication networks. In control engineering too, stochastic approximation is the main paradigm for on-line algorithms for system identification and adaptive control.This is not accidental. The key word in most of these applications is adaptive. Stochastic approximation has several intrinsic traits that make it an attractive framework for adaptive schemes. It is designed for uncertain (read ‘stochastic’) environments, where it allows one to track the ‘average’or ‘typical’behaviour of such an environment. It is incremental, ie, it makes small changes in each step, which ensures a graceful behaviour of the algorithm. This is a highly desirable feature of any adaptive scheme. Furthermore, it usually has low computational and memory requirements per iterate, another desirable feature of adaptive systems. Finally, it conforms to our anthropomorphic notion of adaptation: It makes small adjustments so as to improve a certain performance criterion based on feedback received from the environment.