Stochastic Approximation and Recursive Algorithms and Applications / Edition 2

by Harold Kushner, G. George Yin

Overview

The basic shastic approximation algorithms introduced by Robbins and MonroandbyKieferandWolfowitzintheearly1950shavebeenthesubject 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 defined” shastic processes. The basic paradigm is a shastic difierence 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. Thisbookisconcernedwiththequalitativeandasymptotic 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 finding 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 finding are common in classical numerical analysis, and it is reasonable to expect that appropriate shastic analogs would also perform well.

Product Details

ISBN-13:	9780387008943
Publisher:	Springer New York
Publication date:	07/17/2003
Series:	Stochastic Modelling and Applied Probability , #35
Edition description:	Second Edition 2003
Pages:	478
Product dimensions:	6.10(w) x 9.21(h) x 0.04(d)

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.

Editorial Reviews

From the reviews of the second edition:

"This is the second edition of an excellent book on shastic 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)

From the Publisher