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

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.

FORMAT
Hardcover LANGUAGE
English CONDITION
Brand New Publisher Description

The book 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, with which the asymptotic behavior is characterized by the limit behavior of a mean ODE. 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, general correlated and state-dependent noise, perturbed test function methods, and large devitations methods, are covered. Many motivational examples from learning theory, ergodic cost problems for discrete event systems, wireless communications, adaptive control, signal processing, and elsewhere, illustrate the application of the 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. Harold J. Kushner is a University Professor and Professor of Applied Mathematics at Brown University. He has written numerous books and articles on virtually all aspects of stochastic systems theory, and has received various awards including the IEEE Control Systems Field Award.

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)

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 Text

From the reviews of the second edition: "This is the second edition of an excellent book on stochastic approximation, recursive algorithms and applications a? . Although the structure of the book has not been changed, the authors have thoroughly revised it and added additional material a? ." (Evelyn Buckwar, Zentralblatt MATH, Vol. 1026, 2004)

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 ISBN0387008942 Author Harold Kushner Short Title STOCHASTIC APPROXIMATION & REC Language English Edition 2nd ISBN-10 0387008942 ISBN-13 9780387008943 Media Book Format Hardcover Series Number 35 Year 2003 Imprint Springer-Verlag New York Inc. Place of Publication New York, NY Country of Publication United States Birth 1933 Pages 478 DOI AU Release Date 2003-07-17 NZ Release Date 2003-07-17 US Release Date 2003-07-17 UK Release Date 2003-07-17 Publisher Springer-Verlag New York Inc. Series Stochastic Modelling and Applied Probability Publication Date 2003-07-17 DEWEY 006.31 Audience Undergraduate Illustrations XXII, 478 p. Edition Description Second Edition 2003 Replaces 9781489926982 Country of Origin US Product Class Description Mathematics Alternative 9780387217697
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