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© 2003

Stochastic Approximation and Recursive Algorithms and Applications

Book

Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 35)

About this book

Introduction

 

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.

Keywords

Averaging Markov chain Martingale algorithms diffusion process jump diffusion linear optimization numerical methods optimization programming random walk stability

Authors and affiliations

  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of MathematicsWayne State UniversityDetroitUSA

Bibliographic information

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Reviews

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)