Stochastic Approximation and Recursive Algorithms and Applications

2. Auflage 2003
ISBN: 978-1-4419-1847-5
Verlag: Springer

Buch, Englisch, 478 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 750 g

Reihe: Stochastic Modelling and Applied Probability

The basic stochastic 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 de?ned” stochastic processes. The basic paradigm is a stochastic di?erence 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 ?nding 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 ?nding are common in classical numerical analysis, and it is reasonable to expect that appropriate stochastic analogs would also perform well.

Zielgruppe

Research

Autoren/Hrsg.

Yin, G. George

Kushner, Harold

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Maschinelles Lernen
• Mathematik | Informatik Mathematik Stochastik Elementare Stochastik

Inhaltsverzeichnis

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.