Stochastic Approximation And Optimization Of Random Systems
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Stochastic Approximation and Optimization of Random Systems
The DMV seminar "Stochastische Approximation und Optimierung zufalliger Systeme" was held at Blaubeuren, 28. 5. -4. 6. 1989. The goal was to give an approach to theory and application of stochas tic approximation in view of optimization problems, especially in engineering systems. These notes are based on the seminar lectures. They consist of three parts: I. Foundations of stochastic approximation (H. Walk); n. Applicational aspects of stochastic approximation (G. PHug); In. Applications to adaptation :ugorithms (L. Ljung). The prerequisites for reading this book are basic knowledge in probability, mathematical statistics, optimization. We would like to thank Prof. M. Barner and Prof. G. Fischer for the or ganization of the seminar. We also thank the participants for their cooperation and our assistants and secretaries for typing the manuscript. November 1991 L. Ljung, G. PHug, H. Walk Table of contents I Foundations of stochastic approximation (H. Walk) §1 Almost sure convergence of stochastic approximation procedures 2 §2 Recursive methods for linear problems 17 §3 Stochastic optimization under stochastic constraints 22 §4 A learning model; recursive density estimation 27 §5 Invariance principles in stochastic approximation 30 §6 On the theory of large deviations 43 References for Part I 45 11 Applicational aspects of stochastic approximation (G. PHug) §7 Markovian stochastic optimization and stochastic approximation procedures 53 §8 Asymptotic distributions 71 §9 Stopping times 79 §1O Applications of stochastic approximation methods 80 References for Part II 90 III Applications to adaptation algorithms (L.
Stochastic Approximation and Optimization of Random Systems
The DMV seminar "Stochastische Approximation und Optimierung zufalliger Systeme" was held at Blaubeuren, 28. 5. -4. 6. 1989. The goal was to give an approach to theory and application of stochas tic approximation in view of optimization problems, especially in engineering systems. These notes are based on the seminar lectures. They consist of three parts: I. Foundations of stochastic approximation (H. Walk); n. Applicational aspects of stochastic approximation (G. PHug); In. Applications to adaptation :ugorithms (L. Ljung). The prerequisites for reading this book are basic knowledge in probability, mathematical statistics, optimization. We would like to thank Prof. M. Barner and Prof. G. Fischer for the or ganization of the seminar. We also thank the participants for their cooperation and our assistants and secretaries for typing the manuscript. November 1991 L. Ljung, G. PHug, H. Walk Table of contents I Foundations of stochastic approximation (H. Walk) §1 Almost sure convergence of stochastic approximation procedures 2 §2 Recursive methods for linear problems 17 §3 Stochastic optimization under stochastic constraints 22 §4 A learning model; recursive density estimation 27 §5 Invariance principles in stochastic approximation 30 §6 On the theory of large deviations 43 References for Part I 45 11 Applicational aspects of stochastic approximation (G. PHug) §7 Markovian stochastic optimization and stochastic approximation procedures 53 §8 Asymptotic distributions 71 §9 Stopping times 79 §1O Applications of stochastic approximation methods 80 References for Part II 90 III Applications to adaptation algorithms (L.
Stochastic Approximation and Recursive Algorithms and Applications
Author: Harold Kushner
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-05-04
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.