Stochastic Approximation Algorithms and Applications

✍ Scribed by Harold J. Kushner, G. George Yin (auth.)

• Publisher: Springer New York
• Year: 1997
• Tongue: English
• Leaves: 485
• Series: Applications of Mathematics 35
• Edition: 2nd
• Category: Library

✦ Synopsis

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.

G. George Yin is a Professor of Mathematics at Wayne State University. His research interests focus on applied stochastic processes and stochastic systems theory; he has been a major contributor to stochastic approximation theory.

✦ Table of Contents

Front Matter....Pages i-xxi
Introduction: Applications and Issues....Pages 1-24
Applications to Learning, State Dependent Noise, and Queueing....Pages 25-46
Applications in Signal Processing and Adaptive Control....Pages 47-66
Mathematical Background....Pages 67-83
Convergence with Probability One: Martingale Difference Noise....Pages 85-133
Convergence with Probability One: Correlated Noise....Pages 135-184
Weak Convergence: Introduction....Pages 185-212
Weak Convergence Methods for General Algorithms....Pages 213-250
Applications: Proofs of Convergence....Pages 251-272
Rate of Convergence....Pages 273-325
Averaging of the Iterates....Pages 327-346
Distributed/Decentralized and Asynchronous Algorithms....Pages 347-391
Back Matter....Pages 393-417

✦ Subjects

Probability Theory and Stochastic Processes