Stochastic approximation and recursive algorithms and applications

Harold Kushner, G. George Yin

496 pages, parution le 08/09/2003 (2^eme édition)

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Résumé

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 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.

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.

Introduction: Applications and Issues
Applications to Learning, Repeated Games, State Dependent Noise, and Queue Optimization
Applications to Signal Processing, Communications, and Adaptive Control
Mathematical Background
Convergence w.p.1: Martingale Difference Noise
Convergence w.p.1: 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

References
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Harold Kushner, G. George Yin
Parution	08/09/2003
Édition	2^eme édition
Nb. de pages	496
Format	16 x 24
Couverture	Relié
Poids	835g
Intérieur	Noir et Blanc
EAN13	9780387008943
ISBN13	978-0-387-00894-3