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Stochastic approximation and its applications

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目次 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.
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登録日 2020.06.27
更新日 2020.06.28