Stochastic Approximation and Recursive Algorithms and Applications

  • Harold J. Kushner
  • G. George Yin

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

  • Harold J. Kushner
    • 1
  • G. George Yin
    • 2
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of MathematicsWayne State UniversityDetroitUSA

Bibliographic information

  • DOI https://doi.org/10.1007/b97441
  • Copyright Information Springer-Verlag New York, Inc. 2003
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-00894-3
  • Online ISBN 978-0-387-21769-7
  • Series Print ISSN 0172-4568
  • About this book