Stochastic approximation and recursive algorithms and applications:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY ; Berlin ; Heidelberg
Springer
[2003]
|
| Edition: | second edition |
| Series: | Applications of mathematics
35 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | 1. Aufl. u.d.T.: Kushner, Harold J.: Stochastic approximation algorithms and applications |
| Physical Description: | xxii, 474 Seiten Diagramme |
| ISBN: | 0387008942 9780387008943 9780387217697 |
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| 245 | 1 | 0 | |a Stochastic approximation and recursive algorithms and applications |c Harold J. Kushner ; G. George Yin |
| 250 | |a second edition | ||
| 264 | 1 | |a New York, NY ; Berlin ; Heidelberg |b Springer |c [2003] | |
| 264 | 4 | |c © 2003 | |
| 300 | |a xxii, 474 Seiten |b Diagramme | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applications of mathematics |v 35 | |
| 500 | |a 1. Aufl. u.d.T.: Kushner, Harold J.: Stochastic approximation algorithms and applications | ||
| 650 | 4 | |a Rekursiver Algorithmus | |
| 650 | 4 | |a Stochastische Approximation | |
| 650 | 4 | |a Stochastic approximation | |
| 650 | 4 | |a Recursive functions | |
| 650 | 4 | |a Algorithms | |
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| adam_text | HAROLD J. KUSHNER G. GEORGE YIN STOCHASTIC APPROXIMATION AND RECURSIVE
ALGORITHMS AND APPLICATIONS SECOND EDITION WITH 31 FIGURES SPRINGER
CONTENTS PREFACE AND INTRODUCTION VII INTRODUCTION: APPLICATIONS AND
ISSUES 1 1.0 OUTLINE OF CHAPTER 1 1.1 THE ROBBINS-MONRO ALGORITHM 3
1.1.1 INTRODUCTION 3 1.1.2 FINDING THE ZEROS OF AN UNKNOWN FUNCTION 5
1.1.3 BEST LINEAR LEAST SQUARES FIT 8 1.1.4 MINIMIZATION BY RECURSIVE
MONTE CARLO 12 1.2 THE KIEFER-WOLFOWITZ PROCEDURE 14 1.2.1 THE BASIC
PROCEDURE 14 1.2.2 RANDOM DIRECTIONS 17 1.3 EXTENSIONS OF THE ALGORITHMS
19 1.3.1 A VARIANCE REDUCTION METHOD 19 1.3.2 CONSTRAINTS 21 1.3.3
AVERAGING OF THE ITERATES: POLYAK AVERAGING ... 22 1.3.4 AVERAGING THE
OBSERVATIONS 22 1.3.5 ROBUST ALGORITHMS 23 1.3.6 NONEXISTENCE OF THE
DERIVATIVE AT SOME 9 24 1.3.7 CONVEX OPTIMIZATION AND SUBGRADIENTS 25
1.4 A LAGRANGIAN ALGORITHM FOR CONSTRAINED FUNCTION MINIMIZATION 26
XVIII CONTENTS 2 APPLICATIONS TO LEARNING, REPEATED GAMES, STATE
DEPENDENT NOISE, AND QUEUE OPTIMIZATION 29 2.0 OUTLINE OF CHAPTER 29 2.1
AN ANIMAL LEARNING MODEL 31 2.2 A NEURAL NETWORK 34 2.3 STATE-DEPENDENT
NOISE 37 2.4 LEARNING OPTIMAL CONTROLS 40 2.4.1 Q-LEARNING 41 2.4.2
APPROXIMATING A VALUE FUNCTION 44 2.4.3 PARAMETRIC OPTIMIZATION OF A
MARKOV CHAIN CONTROL PROBLEM 48 2.5 OPTIMIZATION OF A GI/G/1 QUEUE 51
2.5.1 DERIVATIVE ESTIMATION AND INFINITESIMAL PERTURBATION ANALYSIS: A
BRIEF REVIEW 52 2.5.2 THE DERIVATIVE ESTIMATE FOR THE QUEUEING PROBLEM
54 2.6 PASSIVE STOCHASTIC APPROXIMATION 58 2.7 LEARNING IN REPEATED
STOCHASTIC GAMES 59 3 APPLICATIONS IN SIGNAL PROCESSING, COMMUNICATIONS,
AND ADAPTIVE CONTROL 63 3.0 OUTLINE OF CHAPTER 63 3.1 PARAMETER
IDENTIFICATION AND TRACKING 64 3.1.1 THE CLASSICAL MODEL 64 3.1.2 ARMA
AND ARMAX MODELS 68 3.2 TRACKING TIME VARYING SYSTEMS 69 3.2.1 THE
ALGORITHM 69 3.2.2 SOME DATA 73 3.3 FEEDBACK AND AVERAGING 75 3.4
APPLICATIONS IN COMMUNICATIONS THEORY 76 3.4.1 ADAPTIVE NOISE
CANCELLATION AND DISTURBANCE REJECTION 77 3.4.2 ADAPTIVE EQUALIZERS 79
3.4.3 AN ARMA MODEL, WITH A TRAINING SEQUENCE . . . . 80 3.5 ADAPTIVE
ANTENNAS AND MOBILE COMMUNICATIONS 83 3.6 PROPORTIONAL FAIR SHARING 88 4
MATHEMATICAL BACKGROUND 95 4.0 OUTLINE OF CHAPTER 95 4.1 MARTINGALES AND
INEQUALITIES 96 4.2 ORDINARY DIFFERENTIAL EQUATIONS 101 4.2.1 LIMITS OF
A SEQUENCE OF CONTINUOUS FUNCTIONS . . . . 101 4.2.2 STABILITY OF
ORDINARY DIFFERENTIAL EQUATIONS 104 4.3 PROJECTED ODE 106 4.4
COOPERATIVE SYSTEMS AND CHAIN RECURRENCE 110 CONTENTS XIX 4.4.1
COOPERATIVE SYSTEMS 110 4.4.2 CHAIN RECURRENCE 110 4.5 STOCHASTIC
STABILITY 112 CONVERGENCE W.P.L: MARTINGALE DIFFERENCE NOISE 117 5.0
OUTLINE OF CHAPTER 117 5.1 TRUNCATED ALGORITHMS: INTRODUCTION 119 5.2
THE ODE METHOD 125 5.2.1 ASSUMPTIONS AND THE MAIN CONVERGENCE THEOREM
125 5.2.2 CONVERGENCE TO CHAIN RECURRENT POINTS 134 5.3 A GENERAL
COMPACTNESS METHOD 137 5.3.1 THE BASIC CONVERGENCE THEOREM 137 5.3.2
SUFFICIENT CONDITIONS FOR THE RATE OF CHANGE CONDITION 139 5.3.3 THE
KIEFER-WOLFOWITZ ALGORITHM 142 5.4 STABILITY AND COMBINED STABILITY-ODE
METHODS 144 5.4.1 A LIAPUNOV FUNCTION METHOD FOR CONVERGENCE . . . 145
5.4.2 COMBINED STABILITY-ODE METHODS 146 5.5 SOFT CONSTRAINTS 150 5.6
RANDOM DIRECTIONS, SUBGRADIENTS, AND DIFFERENTIAL INCLUSIONS 151 5.7
ANIMAL LEARNING AND PATTERN CLASSIFICATION 154 5.7.1 THE ANIMAL LEARNING
PROBLEM 154 5.7.2 THE PATTERN CLASSIFICATION PROBLEM 156 5.8
NON-CONVERGENCE TO UNSTABLE POINTS 157 CONVERGENCE W.P.L: CORRELATED
NOISE 161 6.0 OUTLINE OF CHAPTER 161 6.1 A GENERAL COMPACTNESS METHOD
162 6.1.1 INTRODUCTION AND GENERAL ASSUMPTIONS 162 6.1.2 THE BASIC
CONVERGENCE THEOREM 166 6.1.3 LOCAL CONVERGENCE RESULTS 169 6.2
SUFFICIENT CONDITIONS 170 6.3 PERTURBED STATE CRITERIA 172 6.3.1
PERTURBED ITERATES 172 6.3.2 GENERAL CONDITIONS FOR THE ASYMPTOTIC RATE
OF CHANGE 175 6.3.3 ALTERNATIVE PERTURBATIONS 177 6.4 EXAMPLES OF STATE
PERTURBATION 180 6.5 KIEFER-WOLFOWITZ ALGORITHMS 183 6.6 STATE-DEPENDENT
NOISE 185 6.7 STABILITY-ODE METHODS 189 6.8 DIFFERENTIAL INCLUSIONS 195
6.9 BOUNDS ON ESCAPE PROBABILITIES 197 CONTENTS 6.10 LARGE DEVIATIONS
201 6.10.1 TWO-SIDED ESTIMATES 202 6.10.2 UPPER BOUNDS 208 6.10.3 BOUNDS
ON ESCAPE TIMES 210 WEAK CONVERGENCE: INTRODUCTION 213 7.0 OUTLINE OF
CHAPTER 213 7.1 INTRODUCTION 215 7.2 MARTINGALE DIFFERENCE NOISE 217 7.3
WEAK CONVERGENCE 226 7.3.1 DEFINITIONS 226 7.3.2 BASIC CONVERGENCE
THEOREMS 229 7.4 MARTINGALE LIMITS 233 7.4.1 VERIFYING THAT A PROCESS IS
A MARTINGALE 233 7.4.2 THE WIENER PROCESS 235 7.4.3 PERTURBED TEST
FUNCTIONS 236 WEAK CONVERGENCE METHODS FOR GENERAL ALGORITHMS 241 8.0
OUTLINE OF CHAPTER 241 8.1 EXOGENOUS NOISE 244 8.2 CONVERGENCE:
EXOGENOUS NOISE 247 8.2.1 CONSTANT STEP SIZE: MARTINGALE DIFFERENCE
NOISE 247 8.2.2 CORRELATED NOISE 255 8.2.3 STEP SIZE E N -» 0 258 8.2.4
RANDOM E N 261 8.2.5 DIFFERENTIAL INCLUSIONS 261 8.2.6 TIME-DEPENDENT
ODES 262 8.3 THE KIEFER-WOLFOWITZ ALGORITHM 263 8.3.1 MARTINGALE
DIFFERENCE NOISE 264 8.3.2 CORRELATED NOISE 265 8.4 STATE-DEPENDENT
NOISE 269 8.4.1 CONSTANT STEP SIZE 270 8.4.2 DECREASING STEP SIZE E N *
0 274 8.4.3 THE INVARIANT MEASURE METHOD 275 8.4.4 GENERAL FORMS OF THE
CONDITIONS 278 8.4.5 OBSERVATIONS DEPENDING ON THE PAST OF THE ITERATE
SEQUENCE OR WORKING DIRECTLY WITH Y 280 8.5 UNCONSTRAINED ALGORITHMS
AND THE ODE-STABILITY METHOD 282 8.6 TWO-TIME-SCALE PROBLEMS 286 8.6.1
THE CONSTRAINED ALGORITHM 286 8.6.2 UNCONSTRAINED ALGORITHMS: STABILITY
288 CONTENTS XXI 9 APPLICATIONS: PROOFS OF CONVERGENCE 291 9.0 OUTLINE
OF CHAPTER 291 9.1 INTRODUCTION 292 9.1.1 GENERAL COMMENTS 292 9.1.2 A
SIMPLE ILLUSTRATIVE SDE EXAMPLE 294 9.2 A SDE EXAMPLE 298 9.3 A DISCRETE
EXAMPLE: A GI/G/1 QUEUE 302 9.4 SIGNAL PROCESSING PROBLEMS 306 9.5
PROPORTIONAL FAIR SHARING 312 10 RATE OF CONVERGENCE 315 10.0 OUTLINE OF
CHAPTER 315 10.1 EXOGENOUS NOISE: CONSTANT STEP SIZE 317 10.1.1
MARTINGALE DIFFERENCE NOISE 317 10.1.2 CORRELATED NOISE 326 10.2
EXOGENOUS NOISE: DECREASING STEP SIZE 328 10.2.1 MARTINGALE DIFFERENCE
NOISE 329 10.2.2 OPTIMAL STEP SIZE SEQUENCE 331 10.2.3 CORRELATED NOISE
332 10.3 KIEFER-WOLFOWITZ ALGORITHM 333 10.3.1 MARTINGALE DIFFERENCE
NOISE 333 10.3.2 CORRELATED NOISE 337 10.4 TIGHTNESS: W.P.I CONVERGENCE
340 10.4.1 MARTINGALE DIFFERENCE NOISE: ROBBINS-MONRO ALGORITHM 340
10.4.2 CORRELATED NOISE 344 10.4.3 KIEFER-WOLFOWITZ ALGORITHM 346 10.5
TIGHTNESS: WEAK CONVERGENCE 347 10.5.1 UNCONSTRAINED ALGORITHM 347
10.5.2 LOCAL METHODS FOR PROVING TIGHTNESS 351 10.6 WEAK CONVERGENCE TO
A WIENER PROCESS 353 10.7 RANDOM DIRECTIONS 358 10.7.1 COMPARISON OF
ALGORITHMS 361 10.8 STATE-DEPENDENT NOISE 365 10.9 LIMIT POINT ON THE
BOUNDARY 369 11 AVERAGING OF THE ITERATES 373 11.0 OUTLINE OF CHAPTER
373 11.1 MINIMAL WINDOW OF AVERAGING 376 11.1.1 ROBBINS-MONRO ALGORITHM:
DECREASING STEP SIZE 376 11.1.2 CONSTANT STEP SIZE 379 11.1.3 AVERAGING
WITH FEEDBACK AND CONSTANT STEP SIZE 380 11.1.4 KIEFER-WOLFOWITZ
ALGORITHM 381 XXII CONTENTS 11.2 A TWO-TIME-SCALE INTERPRETATION 382
11.3 MAXIMAL WINDOW OF AVERAGING 383 11.4 THE PARAMETER IDENTIFICATION
PROBLEM 391 12 DISTRIBUTED/DECENTRALIZED AND ASYNCHRONOUS ALGORITHMS 395
12.0 OUTLINE OF CHAPTER 395 12.1 EXAMPLES 397 12.1.1 INTRODUCTORY
COMMENTS 397 12.1.2 PIPELINED COMPUTATIONS 398 12.1.3 A DISTRIBUTED AND
DECENTRALIZED NETWORK MODEL 400 12.1.4 MULTIACCESS COMMUNICATIONS 402
12.2 REAL-TIME SCALE: INTRODUCTION 403 12.3 THE BASIC ALGORITHMS 408
12.3.1 CONSTANT STEP SIZE: INTRODUCTION 408 12.3.2 MARTINGALE DIFFERENCE
NOISE 410 12.3.3 CORRELATED NOISE 417 12.3.4 ANALYSIS FOR E - * 0 AND T
-5- OO 419 12.4 DECREASING STEP SIZE 421 12.5 STATE-DEPENDENT NOISE 428
12.6 RATE OF CONVERGENCE 430 12.7 STABILITY AND TIGHTNESS OF THE
NORMALIZED ITERATES 436 12.7.1 UNCONSTRAINED ALGORITHMS 436 12.8
CONVERGENCE FOR Q-LEARNING: DISCOUNTED COST 439 REFERENCES 443 SYMBOL
INDEX 465 SUBJECT INDEX 469
|
| adam_txt |
HAROLD J. KUSHNER G. GEORGE YIN STOCHASTIC APPROXIMATION AND RECURSIVE
ALGORITHMS AND APPLICATIONS SECOND EDITION WITH 31 FIGURES SPRINGER
CONTENTS PREFACE AND INTRODUCTION VII INTRODUCTION: APPLICATIONS AND
ISSUES 1 1.0 OUTLINE OF CHAPTER 1 1.1 THE ROBBINS-MONRO ALGORITHM 3
1.1.1 INTRODUCTION 3 1.1.2 FINDING THE ZEROS OF AN UNKNOWN FUNCTION 5
1.1.3 BEST LINEAR LEAST SQUARES FIT 8 1.1.4 MINIMIZATION BY RECURSIVE
MONTE CARLO 12 1.2 THE KIEFER-WOLFOWITZ PROCEDURE 14 1.2.1 THE BASIC
PROCEDURE 14 1.2.2 RANDOM DIRECTIONS 17 1.3 EXTENSIONS OF THE ALGORITHMS
19 1.3.1 A VARIANCE REDUCTION METHOD 19 1.3.2 CONSTRAINTS 21 1.3.3
AVERAGING OF THE ITERATES: "POLYAK AVERAGING" . 22 1.3.4 AVERAGING THE
OBSERVATIONS 22 1.3.5 ROBUST ALGORITHMS 23 1.3.6 NONEXISTENCE OF THE
DERIVATIVE AT SOME 9 24 1.3.7 CONVEX OPTIMIZATION AND SUBGRADIENTS 25
1.4 A LAGRANGIAN ALGORITHM FOR CONSTRAINED FUNCTION MINIMIZATION 26
XVIII CONTENTS 2 APPLICATIONS TO LEARNING, REPEATED GAMES, STATE
DEPENDENT NOISE, AND QUEUE OPTIMIZATION 29 2.0 OUTLINE OF CHAPTER 29 2.1
AN ANIMAL LEARNING MODEL 31 2.2 A NEURAL NETWORK 34 2.3 STATE-DEPENDENT
NOISE 37 2.4 LEARNING OPTIMAL CONTROLS 40 2.4.1 Q-LEARNING 41 2.4.2
APPROXIMATING A VALUE FUNCTION 44 2.4.3 PARAMETRIC OPTIMIZATION OF A
MARKOV CHAIN CONTROL PROBLEM 48 2.5 OPTIMIZATION OF A GI/G/1 QUEUE 51
2.5.1 DERIVATIVE ESTIMATION AND INFINITESIMAL PERTURBATION ANALYSIS: A
BRIEF REVIEW 52 2.5.2 THE DERIVATIVE ESTIMATE FOR THE QUEUEING PROBLEM
54 2.6 PASSIVE STOCHASTIC APPROXIMATION 58 2.7 LEARNING IN REPEATED
STOCHASTIC GAMES 59 3 APPLICATIONS IN SIGNAL PROCESSING, COMMUNICATIONS,
AND ADAPTIVE CONTROL 63 3.0 OUTLINE OF CHAPTER 63 3.1 PARAMETER
IDENTIFICATION AND TRACKING 64 3.1.1 THE CLASSICAL MODEL 64 3.1.2 ARMA
AND ARMAX MODELS 68 3.2 TRACKING TIME VARYING SYSTEMS 69 3.2.1 THE
ALGORITHM 69 3.2.2 SOME DATA 73 3.3 FEEDBACK AND AVERAGING 75 3.4
APPLICATIONS IN COMMUNICATIONS THEORY 76 3.4.1 ADAPTIVE NOISE
CANCELLATION AND DISTURBANCE REJECTION 77 3.4.2 ADAPTIVE EQUALIZERS 79
3.4.3 AN ARMA MODEL, WITH A TRAINING SEQUENCE . . . . 80 3.5 ADAPTIVE
ANTENNAS AND MOBILE COMMUNICATIONS 83 3.6 PROPORTIONAL FAIR SHARING 88 4
MATHEMATICAL BACKGROUND 95 4.0 OUTLINE OF CHAPTER 95 4.1 MARTINGALES AND
INEQUALITIES 96 4.2 ORDINARY DIFFERENTIAL EQUATIONS 101 4.2.1 LIMITS OF
A SEQUENCE OF CONTINUOUS FUNCTIONS . . . . 101 4.2.2 STABILITY OF
ORDINARY DIFFERENTIAL EQUATIONS 104 4.3 PROJECTED ODE 106 4.4
COOPERATIVE SYSTEMS AND CHAIN RECURRENCE 110 CONTENTS XIX 4.4.1
COOPERATIVE SYSTEMS 110 4.4.2 CHAIN RECURRENCE 110 4.5 STOCHASTIC
STABILITY 112 CONVERGENCE W.P.L: MARTINGALE DIFFERENCE NOISE 117 5.0
OUTLINE OF CHAPTER 117 5.1 TRUNCATED ALGORITHMS: INTRODUCTION 119 5.2
THE ODE METHOD 125 5.2.1 ASSUMPTIONS AND THE MAIN CONVERGENCE THEOREM
125 5.2.2 CONVERGENCE TO CHAIN RECURRENT POINTS 134 5.3 A GENERAL
COMPACTNESS METHOD 137 5.3.1 THE BASIC CONVERGENCE THEOREM 137 5.3.2
SUFFICIENT CONDITIONS FOR THE RATE OF CHANGE CONDITION 139 5.3.3 THE
KIEFER-WOLFOWITZ ALGORITHM 142 5.4 STABILITY AND COMBINED STABILITY-ODE
METHODS 144 5.4.1 A LIAPUNOV FUNCTION METHOD FOR CONVERGENCE . . . 145
5.4.2 COMBINED STABILITY-ODE METHODS 146 5.5 SOFT CONSTRAINTS 150 5.6
RANDOM DIRECTIONS, SUBGRADIENTS, AND DIFFERENTIAL INCLUSIONS 151 5.7
ANIMAL LEARNING AND PATTERN CLASSIFICATION 154 5.7.1 THE ANIMAL LEARNING
PROBLEM 154 5.7.2 THE PATTERN CLASSIFICATION PROBLEM 156 5.8
NON-CONVERGENCE TO UNSTABLE POINTS 157 CONVERGENCE W.P.L: CORRELATED
NOISE 161 6.0 OUTLINE OF CHAPTER 161 6.1 A GENERAL COMPACTNESS METHOD
162 6.1.1 INTRODUCTION AND GENERAL ASSUMPTIONS 162 6.1.2 THE BASIC
CONVERGENCE THEOREM 166 6.1.3 LOCAL CONVERGENCE RESULTS 169 6.2
SUFFICIENT CONDITIONS 170 6.3 PERTURBED STATE CRITERIA 172 6.3.1
PERTURBED ITERATES 172 6.3.2 GENERAL CONDITIONS FOR THE ASYMPTOTIC RATE
OF CHANGE 175 6.3.3 ALTERNATIVE PERTURBATIONS 177 6.4 EXAMPLES OF STATE
PERTURBATION 180 6.5 KIEFER-WOLFOWITZ ALGORITHMS 183 6.6 STATE-DEPENDENT
NOISE 185 6.7 STABILITY-ODE METHODS 189 6.8 DIFFERENTIAL INCLUSIONS 195
6.9 BOUNDS ON ESCAPE PROBABILITIES 197 CONTENTS 6.10 LARGE DEVIATIONS
201 6.10.1 TWO-SIDED ESTIMATES 202 6.10.2 UPPER BOUNDS 208 6.10.3 BOUNDS
ON ESCAPE TIMES 210 WEAK CONVERGENCE: INTRODUCTION 213 7.0 OUTLINE OF
CHAPTER 213 7.1 INTRODUCTION 215 7.2 MARTINGALE DIFFERENCE NOISE 217 7.3
WEAK CONVERGENCE 226 7.3.1 DEFINITIONS 226 7.3.2 BASIC CONVERGENCE
THEOREMS 229 7.4 MARTINGALE LIMITS 233 7.4.1 VERIFYING THAT A PROCESS IS
A MARTINGALE 233 7.4.2 THE WIENER PROCESS 235 7.4.3 PERTURBED TEST
FUNCTIONS 236 WEAK CONVERGENCE METHODS FOR GENERAL ALGORITHMS 241 8.0
OUTLINE OF CHAPTER 241 8.1 EXOGENOUS NOISE 244 8.2 CONVERGENCE:
EXOGENOUS NOISE 247 8.2.1 CONSTANT STEP SIZE: MARTINGALE DIFFERENCE
NOISE 247 8.2.2 CORRELATED NOISE 255 8.2.3 STEP SIZE E N -» 0 258 8.2.4
RANDOM E N 261 8.2.5 DIFFERENTIAL INCLUSIONS 261 8.2.6 TIME-DEPENDENT
ODES 262 8.3 THE KIEFER-WOLFOWITZ ALGORITHM 263 8.3.1 MARTINGALE
DIFFERENCE NOISE 264 8.3.2 CORRELATED NOISE 265 8.4 STATE-DEPENDENT
NOISE 269 8.4.1 CONSTANT STEP SIZE 270 8.4.2 DECREASING STEP SIZE E N *
0 274 8.4.3 THE INVARIANT MEASURE METHOD 275 8.4.4 GENERAL FORMS OF THE
CONDITIONS 278 8.4.5 OBSERVATIONS DEPENDING ON THE PAST OF THE ITERATE
SEQUENCE OR WORKING DIRECTLY WITH Y 280 8.5 UNCONSTRAINED ALGORITHMS
AND THE ODE-STABILITY METHOD 282 8.6 TWO-TIME-SCALE PROBLEMS 286 8.6.1
THE CONSTRAINED ALGORITHM 286 8.6.2 UNCONSTRAINED ALGORITHMS: STABILITY
288 CONTENTS XXI 9 APPLICATIONS: PROOFS OF CONVERGENCE 291 9.0 OUTLINE
OF CHAPTER 291 9.1 INTRODUCTION 292 9.1.1 GENERAL COMMENTS 292 9.1.2 A
SIMPLE ILLUSTRATIVE SDE EXAMPLE 294 9.2 A SDE EXAMPLE 298 9.3 A DISCRETE
EXAMPLE: A GI/G/1 QUEUE 302 9.4 SIGNAL PROCESSING PROBLEMS 306 9.5
PROPORTIONAL FAIR SHARING 312 10 RATE OF CONVERGENCE 315 10.0 OUTLINE OF
CHAPTER 315 10.1 EXOGENOUS NOISE: CONSTANT STEP SIZE 317 10.1.1
MARTINGALE DIFFERENCE NOISE 317 10.1.2 CORRELATED NOISE 326 10.2
EXOGENOUS NOISE: DECREASING STEP SIZE 328 10.2.1 MARTINGALE DIFFERENCE
NOISE 329 10.2.2 OPTIMAL STEP SIZE SEQUENCE 331 10.2.3 CORRELATED NOISE
332 10.3 KIEFER-WOLFOWITZ ALGORITHM 333 10.3.1 MARTINGALE DIFFERENCE
NOISE 333 10.3.2 CORRELATED NOISE 337 10.4 TIGHTNESS: W.P.I CONVERGENCE
340 10.4.1 MARTINGALE DIFFERENCE NOISE: ROBBINS-MONRO ALGORITHM 340
10.4.2 CORRELATED NOISE 344 10.4.3 KIEFER-WOLFOWITZ ALGORITHM 346 10.5
TIGHTNESS: WEAK CONVERGENCE 347 10.5.1 UNCONSTRAINED ALGORITHM 347
10.5.2 LOCAL METHODS FOR PROVING TIGHTNESS 351 10.6 WEAK CONVERGENCE TO
A WIENER PROCESS 353 10.7 RANDOM DIRECTIONS 358 10.7.1 COMPARISON OF
ALGORITHMS 361 10.8 STATE-DEPENDENT NOISE 365 10.9 LIMIT POINT ON THE
BOUNDARY 369 11 AVERAGING OF THE ITERATES 373 11.0 OUTLINE OF CHAPTER
373 11.1 MINIMAL WINDOW OF AVERAGING 376 11.1.1 ROBBINS-MONRO ALGORITHM:
DECREASING STEP SIZE 376 11.1.2 CONSTANT STEP SIZE 379 11.1.3 AVERAGING
WITH FEEDBACK AND CONSTANT STEP SIZE 380 11.1.4 KIEFER-WOLFOWITZ
ALGORITHM 381 XXII CONTENTS 11.2 A TWO-TIME-SCALE INTERPRETATION 382
11.3 MAXIMAL WINDOW OF AVERAGING 383 11.4 THE PARAMETER IDENTIFICATION
PROBLEM 391 12 DISTRIBUTED/DECENTRALIZED AND ASYNCHRONOUS ALGORITHMS 395
12.0 OUTLINE OF CHAPTER 395 12.1 EXAMPLES 397 12.1.1 INTRODUCTORY
COMMENTS 397 12.1.2 PIPELINED COMPUTATIONS 398 12.1.3 A DISTRIBUTED AND
DECENTRALIZED NETWORK MODEL 400 12.1.4 MULTIACCESS COMMUNICATIONS 402
12.2 REAL-TIME SCALE: INTRODUCTION 403 12.3 THE BASIC ALGORITHMS 408
12.3.1 CONSTANT STEP SIZE: INTRODUCTION 408 12.3.2 MARTINGALE DIFFERENCE
NOISE 410 12.3.3 CORRELATED NOISE 417 12.3.4 ANALYSIS FOR E - * 0 AND T
-5- OO 419 12.4 DECREASING STEP SIZE 421 12.5 STATE-DEPENDENT NOISE 428
12.6 RATE OF CONVERGENCE 430 12.7 STABILITY AND TIGHTNESS OF THE
NORMALIZED ITERATES 436 12.7.1 UNCONSTRAINED ALGORITHMS 436 12.8
CONVERGENCE FOR Q-LEARNING: DISCOUNTED COST 439 REFERENCES 443 SYMBOL
INDEX 465 SUBJECT INDEX 469 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Kushner, Harold J. 1933- Yin, George 1954- |
| author_GND | (DE-588)11559163X (DE-588)115596798 |
| author_facet | Kushner, Harold J. 1933- Yin, George 1954- |
| author_role | aut aut |
| author_sort | Kushner, Harold J. 1933- |
| author_variant | h j k hj hjk g y gy |
| building | Verbundindex |
| bvnumber | BV023562076 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.2.K88 2003 |
| callnumber-search | QA274.2.K88 2003 |
| callnumber-sort | QA 3274.2 K88 42003 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 440 SK 820 |
| ctrlnum | (OCoLC)249217081 (DE-599)BVBBV023562076 |
| dewey-full | 519.221 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 21 519.2 |
| dewey-search | 519.2 21 519.2 |
| dewey-sort | 3519.2 221 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | second edition |
| format | Book |
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| id | DE-604.BV023562076 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:38:00Z |
| indexdate | 2024-07-09T21:24:34Z |
| institution | BVB |
| isbn | 0387008942 9780387008943 9780387217697 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016878411 |
| oclc_num | 249217081 |
| open_access_boolean | |
| owner | DE-521 DE-473 DE-BY-UBG DE-83 DE-355 DE-BY-UBR DE-11 DE-188 DE-739 DE-20 DE-634 DE-898 DE-BY-UBR |
| owner_facet | DE-521 DE-473 DE-BY-UBG DE-83 DE-355 DE-BY-UBR DE-11 DE-188 DE-739 DE-20 DE-634 DE-898 DE-BY-UBR |
| physical | xxii, 474 Seiten Diagramme |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer |
| record_format | marc |
| series | Applications of mathematics |
| series2 | Applications of mathematics |
| spelling | Kushner, Harold J. 1933- (DE-588)11559163X aut Stochastic approximation and recursive algorithms and applications Harold J. Kushner ; G. George Yin second edition New York, NY ; Berlin ; Heidelberg Springer [2003] © 2003 xxii, 474 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Applications of mathematics 35 1. Aufl. u.d.T.: Kushner, Harold J.: Stochastic approximation algorithms and applications Rekursiver Algorithmus Stochastische Approximation Stochastic approximation Recursive functions Algorithms Rekursiver Algorithmus (DE-588)4502357-8 gnd rswk-swf Stochastische Approximation (DE-588)4183371-5 gnd rswk-swf Stochastische Approximation (DE-588)4183371-5 s DE-604 Rekursiver Algorithmus (DE-588)4502357-8 s Yin, George 1954- (DE-588)115596798 aut Erscheint auch als Online-Ausgabe 978-0-387-21769-7 Applications of mathematics 35 (DE-604)BV000895226 35 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016878411&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kushner, Harold J. 1933- Yin, George 1954- Stochastic approximation and recursive algorithms and applications Applications of mathematics Rekursiver Algorithmus Stochastische Approximation Stochastic approximation Recursive functions Algorithms Rekursiver Algorithmus (DE-588)4502357-8 gnd Stochastische Approximation (DE-588)4183371-5 gnd |
| subject_GND | (DE-588)4502357-8 (DE-588)4183371-5 |
| title | Stochastic approximation and recursive algorithms and applications |
| title_auth | Stochastic approximation and recursive algorithms and applications |
| title_exact_search | Stochastic approximation and recursive algorithms and applications |
| title_exact_search_txtP | Stochastic approximation and recursive algorithms and applications |
| title_full | Stochastic approximation and recursive algorithms and applications Harold J. Kushner ; G. George Yin |
| title_fullStr | Stochastic approximation and recursive algorithms and applications Harold J. Kushner ; G. George Yin |
| title_full_unstemmed | Stochastic approximation and recursive algorithms and applications Harold J. Kushner ; G. George Yin |
| title_short | Stochastic approximation and recursive algorithms and applications |
| title_sort | stochastic approximation and recursive algorithms and applications |
| topic | Rekursiver Algorithmus Stochastische Approximation Stochastic approximation Recursive functions Algorithms Rekursiver Algorithmus (DE-588)4502357-8 gnd Stochastische Approximation (DE-588)4183371-5 gnd |
| topic_facet | Rekursiver Algorithmus Stochastische Approximation Stochastic approximation Recursive functions Algorithms |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016878411&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000895226 |
| work_keys_str_mv | AT kushnerharoldj stochasticapproximationandrecursivealgorithmsandapplications AT yingeorge stochasticapproximationandrecursivealgorithmsandapplications |