Stochastic approximation and its applications
By: by Han-Fu Chen.
Series: Nonconvex optimization and its applications -- v. 64
Publisher: Kluwer Academic Publishers
Published: 2002
Place of publication: Dordrecht; Boston
Language: eng
Number of pages: 357
Subjects: Stochastic approximation.
Description: This book presents the recent development of stochastic approximation algorithms with expanding truncations based on the TS (trajectory-subsequence) method, a newly developed method for convergence analysis. This approach is so powerful that conditions used for guaranteeing convergence have been considerably weakened in comparison with those applied in the classical probability and ODE methods. The general convergence theorem is presented for sample paths and is proved in a purely deterministic way. The sample-path description of theorems is particularly convenient for applications. Convergence theory takes both observation noise and structural error of the regression function into consideration. Convergence rates, asymptotic normality and other asymptotic properties are presented as well. Applications of the developed theory to global optimization, blind channel identification, adaptive filtering, system parameter identification, adaptive stabilization and other problems arising from engineering fields are demonstrated.
Notes: Includes bibliographical references (p. 347-353) and index.
Table of contents: title: Machine generated contents note: Preface Acknowledgments 1. ROBBINS-MONRO ALGORITHM 1.1 Finding Zeros of a Function. 1.2 Probabilistic Method 1.3 ODE Method 1.4 Truncated RM Algorithm and TS Method 1.5 Weak Convergence Method 1.6 Notes and References 2. STOCHASTIC APPROXIMATION ALGORITHMS WITH EXPANDING TRUNCATIONS 2.1 Motivation 2.2 General Convergence Theorems by TS Method 2.3 Convergence Under State-Independent Conditions 2.4 Necessity of Noise Condition 2.5 Non-Additive Noise 2.6 Connection Between Trajectory Convergence and Proper of Limit Points 2.7 Robustness of Stochastic Approximation Algorithms 2.8 Dynamic Stochastic Approximation 2.9 Notes and References 3. ASYMPTOTIC PROPERTIES OF STOCHASTIC APPROXIMATION ALGORITHMS 3.1 Convergence Rate: Nondegenerate Case 3.2 Convergence Rate: Degenerate Case 3.3 Asymptotic Normality STOCHASTIC APPROXIMATION AND ITS APPLICATIONS 3.4 Asymptotic Efficiency 3.5 Notes and References 4. OPTIMIZATION BY STOCHASTIC APPROXIMATION 4.1 Kiefer-Wolfowitz Algorithm with Randomized Differences 4.2 Asymptotic Properties of KW Algorithm 4.3 Global Optimization 4.4 Asymptotic Behavior of Global Optimization Algorithm 4.5 Application to Model Reduction 4.6 Notes and References 5. APPLICATION TO SIGNAL PROCESSING 5.1 Recursive Blind Identification 5.2 Principal Component Analysis 5.3 Recursive Blind Identification by PCA 5.4 Constrained Adaptive Filtering 5.5 Adaptive Filtering by Sign Algorithms 5.6 Asynchronous Stochastic Approximation 5.7 Notes and References 6. APPLICATION TO SYSTEMS AND CONTROL 6.1 Application to Identification and Adaptive Control 6.2 Application to Adaptive Stabilization 6.3 Application to Pole Assignment for Systems with Unknown Coefficients 6.4 Application to Adaptive Regulation 6.5 Notes and References Appendices A.1 Probability Space A.2 Random Variable and Distribution Function A.3 Expectation A.4 Convergence Theorems and Inequalities A.5 Conditional Expectation A.6 Independence A.7 Ergodicity B.1 Convergence Theorems for Martingale B.2 Convergence Theorems for MDS I B.3 Borel-Cantelli-L6vy Lemma B.4 Convergence Criteria for Adapted Sequences B.5 Convergence Theorems for MDS II B.6 Weighted Sum of MDS References.