Stochastic Approximation and Recursive Algorithms and Applications by G. George

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Stochastic Approximation and Recursive Algorithms and Applications by G. George Yin, Harold Kushner

takes n+1 n n n n its values in some Euclidean space, Y is a random variable, and the "step n size" > 0 is small and might go to zero as n??.

FORMAT
Paperback LANGUAGE
English CONDITION
Brand New Publisher Description

The basic stochastic approximation algorithms introduced by Robbins and of an enormous literature, both theoretical and applied. This is due to the large number of applications and the interesting theoretical issues in the analysis of "dynamically de?ned" stochastic processes. The basic paradigm is a stochastic di?erence equation such as ? = ? + Y , where ? takes n+1 n n n n its values in some Euclidean space, Y is a random variable, and the "step n size" > 0 is small and might go to zero as n??. In its simplest form, n ? is a parameter of a system, and the random vector Y is a function of n "noise-corrupted" observations taken on the system when the parameter is set to ? . One recursively adjusts the parameter so that some goal is met n asymptotically. properties of such recursive algorithms in the diverse forms in which they arise in applications. There are analogous continuous time algorithms, but the conditions and proofs are generally very close to those for the discrete time case. The original work was motivated by the problem of ?nding a root of a continuous function g ¯(?), where the function is not known but the - perimenter is able to take "noisy" measurements at any desired value of ?. Recursive methods for root ?nding are common in classical numerical analysis, and it is reasonable to expect that appropriate stochastic analogs would also perform well.

Notes

The book presents a thorough development of the modern theory of
stochastic approximation or recursive stochastic algorithms for both
constrained and unconstrained problems. The assumptions and proof
methods are designed to cover the needs of recent applications. The
development proceeds from simple to complex problems, allowing the
underlying ideas to be more easily understood. Many examples
illustrate the application of the theory.
This second edition is a thorough revision, although the main features
and the structure remain unchanged. It contains many additional
applications and results, and more detailed discussion.

Back Cover

This revised and expanded second edition presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. There is a complete development of both probability one and weak convergence methods for very general noise processes. The proofs of convergence use the ODE method, the most powerful to date. The assumptions and proof methods are designed to cover the needs of recent applications. The development proceeds from simple to complex problems, allowing the underlying ideas to be more easily understood. Rate of convergence, iterate averaging, high-dimensional problems, stability-ODE methods, two time scale, asynchronous and decentralized algorithms, state-dependent noise, stability methods for correlated noise, perturbed test function methods, and large deviations methods are covered. Many motivating examples from learning theory, ergodic cost problems for discrete event systems, wireless communications, adaptive control, signal processing, and elsewhere illustrate the applications of the theory.

Table of Contents

Introduction: Applications and Issues.- Applications to Learning, Repeated Games, State Dependent Noise, and Queue Optimization.- Applications in Signal Processing, Communications, and Adaptive Control.- Mathematical Background.- Convergence with Probability One: Martingale Difference Noise.- Convergence with Probability One: Correlated Noise.- Weak Convergence: Introduction.- Weak Convergence Methods for General Algorithms.- Applications: Proofs of Convergence.- Rate of Convergence.- Averaging of the Iterates.- Distributed/Decentralized and Asynchronous Algorithms.

Review

From the reviews of the second edition:"This is the second edition of an excellent book on stochastic approximation, recursive algorithms and applications … . Although the structure of the book has not been changed, the authors have thoroughly revised it and added additional material … ." (Evelyn Buckwar, Zentralblatt MATH, Vol. 1026, 2004)"The book attempts to convince that … algorithms naturally arise in many application areas … . I do not hesitate to conclude that this book is exceptionally well written. The literature citation is extensive, and pertinent to the topics at hand, throughout. This book could be well suited to those at the level of the graduate researcher and upwards." (A. C. Brooms, Journal of the Royal Statistical Society Series A: Statistics in Society, Vol. 169 (3), 2006)

Promotional

2nd edition

Long Description

The basic stochastic approximation algorithms introduced by Robbins and of an enormous literature, both theoretical and applied. This is due to the large number of applications and the interesting theoretical issues in the analysis of "dynamically de'ned" stochastic processes. The basic paradigm is a stochastic di'erence equation such as ? = ? + Y , where ? takes n+1 n n n n its values in some Euclidean space, Y is a random variable, and the "step n size" > 0 is small and might go to zero as n?'. In its simplest form, n ? is a parameter of a system, and the random vector Y is a function of n "noise-corrupted" observations taken on the system when the parameter is set to ? . One recursively adjusts the parameter so that some goal is met n asymptotically. properties of such recursive algorithms in the diverse forms in which they arise in applications. There are analogous continuous time algorithms, but the conditions and proofs are generally very close to those for the discrete time case. The original work was motivated by the problem of ?nding a root of a continuous function g

Review Quote

From the reviews of the second edition:"This is the second edition of an excellent book on stochastic approximation, recursive algorithms and applications … . Although the structure of the book has not been changed, the authors have thoroughly revised it and added additional material … ." (Evelyn Buckwar, Zentralblatt MATH, Vol. 1026, 2004)"The book attempts to convince that … algorithms naturally arise in many application areas … . I do not hesitate to conclude that this book is exceptionally well written. The literature citation is extensive, and pertinent to the topics at hand, throughout. This book could be well suited to those at the level of the graduate researcher and upwards." (A. C. Brooms, Journal of the Royal Statistical Society Series A: Statistics in Society, Vol. 169 (3), 2006)

Feature

Includes supplementary material:

Description for Sales People

The book presents a thorough development of the modern theory ofstochastic approximation or recursive stochastic algorithms for bothconstrained and unconstrained problems. The assumptions and proofmethods are designed to cover the needs of recent applications. Thedevelopment proceeds from simple to complex problems, allowing theunderlying ideas to be more easily understood. Many examplesillustrate the application of the second edition is a thorough revision, although the main featuresand the structure remain unchanged. It contains many additionalapplications and results, and more detailed discussion.

Details ISBN1441918477 Author Harold Kushner Publisher Springer-Verlag New York Inc. Series Stochastic Modelling and Applied Probability Year 2010 ISBN-10 1441918477 ISBN-13 9781441918475 Format Paperback Imprint Springer-Verlag New York Inc. Place of Publication New York, NY Country of Publication United States DEWEY 510 Short Title STOCHASTIC APPROXIMATION & REC Language English Edition 2nd Media Book Series Number 35 Publication Date 2010-11-24 Pages 478 UK Release Date 2010-11-24 AU Release Date 2010-11-24 NZ Release Date 2010-11-24 US Release Date 2010-11-24 Alternative 9780387008943 Audience Professional & Vocational Replaces 9781489926982 Illustrations XXII, 478 p. Edition Description Second Edition 2003 Country of Origin NL Product Class Description Mathematics
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