Introduction to stochastic search and optimization: estimation, simulation, and control
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley-Interscience
2003
|
| Schriftenreihe: | Wiley-Interscience series in discrete mathematics and optimization
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Publisher description Table of contents Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 558-579) and index |
| Beschreibung: | xx, 595 S. graph. Darst. |
| ISBN: | 0471330523 |
Internformat
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| 100 | 1 | |a Spall, James C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to stochastic search and optimization |b estimation, simulation, and control |c James C. Spall |
| 264 | 1 | |a Hoboken, NJ |b Wiley-Interscience |c 2003 | |
| 300 | |a xx, 595 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley-Interscience series in discrete mathematics and optimization | |
| 500 | |a Includes bibliographical references (p. 558-579) and index | ||
| 650 | 4 | |a Décision, Théorie de la | |
| 650 | 7 | |a Optimaliseren |2 gtt | |
| 650 | 4 | |a Optimisation mathématique | |
| 650 | 4 | |a Processus stochastiques | |
| 650 | 7 | |a Stochastische processen |2 gtt | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Search theory | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 0 | 7 | |a Stochastik |0 (DE-588)4121729-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastische Optimierung |0 (DE-588)4057625-5 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804129581056131072 |
|---|---|
| adam_text | Contents
Preface
............................................................................................................
хні
1.
Stochastic Search and Optimization: Motivation and Supporting
Results
................................................................................................... 1
1.1
Introduction
................................................................................... 1
1.1.1
General Background
......................................................... 1
1.1.2
Formal Problem Statement; General Types of
Problems and Solutions; Global versus Local Search
...... 3
1.1.3
Meaning of Stochastic in Stochastic Search and
Optimization
..................................................................... 7
1.2
Some Principles of Stochastic Search and Optimization
.............. 12
1.2.1
Some Key Points
............................................................... 13
1.2.2
Limits of Performance: No Free Lunch
Theorems
........................................................................... 18
1.3
Gradients, Hessians, and Their Connection to Optimization of
Smooth Functions
...................................................................... 20
1.3.1
Definition of Gradient and Hessian in the Context of
Loss Functions
.................................................................. 20
1.3.2
First- and Second-Order Conditions for Optimization
..... 21
1.4
Deterministic Search and Optimization: Steepest Descent and
Newton-Raphson Search
.............................................................. 22
1.4.1
Steepest Descent Method
.................................................. 22
1.4.2
Newton-Raphson Method and Deterministic
Convergence Rates.....
....................................................... 27
1.5
Concluding Remarks
..................................................................... 30
Exercises
................................................................................................ 31
2.
Direct Methods for Stochastic Search
............................................... 34
2.1
Introduction
................................................................................... 34
2.2
Random Search with Noise-Free Loss Measurements
................. 36
2.2.1
Some Attributes of Direct Random Search
....................... 36
2.2.2
Three Algorithms for Random Search
.............................. 37
2.2.3
Example Implementations
................................................. 46
vi
Contents
2.3
Random Search with Noisy Loss Measurements
.......................... 50
2.4
Nonlinear Simplex (Nelder-Mead) Algorithm
............................. 55
2.4.1
Basic Method
.................................................................... 55
2.4.2
Adaptation for Noisy Loss Measurements
........................ 58
2.5
Concluding Remarks
..................................................................... 60
Exercises
................................................................................................ 61
3.
Recursive Estimation for Linear Models
........................................... 65
3.1
Formulation for Estimation with Linear Models
.......................... 65
3.1.1
Linear Model.
.................................................................... 66
3.1.2
Mean-Squared and Least-Squares Estimation
.................. 68
3.2
Least-Mean-Squares and Recursive-Least-Squares
for Static
θ
.................................................................................... 72
3.2.1
Introduction
....................................................................... 72
3.2.2
Basic LMS Algorithm
....................................................... 73
3.2.3
LMS Algorithm in Adaptive Signal Processing and
Control
.............................................................................. 75
3.2.4
Basic RLS Algorithm
........................................................ 87
3.2.5
Connection of RLS to the Newton-Raphson Method
...... 81
3.2.6
Extensions to Multivariate RLS and Weighted
Summands in Least-Squares Criterion
.............................. 82
3.3
LMS, RLS, and
Kalman
Filter for Time-Varying
θ
..................... 83
3.3.1
Introduction
....................................................................... 83
3.3.2
LMS
.................................................................................. 85
3.3.3
RLS.....
.............................................................................. 86
3.3.4
Kalman
Filter
.................................................................... 87
3.4
Case Study: Analysis of Oboe Reed Data
..................................... 88
3.5
Concluding Remarks
..................................................................... 92
Exercises
................................................................................................ 93
4.
Stochastic Approximation for Nonlinear Root-Finding...................
95
4.1
Introduction
................................................................................... 95
4.2
Potpourri of Stochastic Approximation Examples
....................... 98
4.3
Convergence of Stochastic Approximation
.................................. 104
4.3.1
Background...
.................................................................... 104
4.3.2
Convergence Conditions
.................................................. 105
4.3.3
On the Gain Sequence and Connection to ODEs
............. 108
4.4
Asymptotic Normality and Choice of Gain Sequence
..................
Ill
4.5
Extensions to Basic Stochastic Approximation
............................ 115
4.5.1
Joint Parameter and State Evolution
................................. 115
4.5.2
Adaptive Estimation and Higher-Order Algorithms.........
116
Contents
vii
4.5.3
Iterate
Averaging
............................................................... 117
4.5.4
Time-Varying Functions
................................................... 120
4.6
Concluding Remarks
..................................................................... 121
Exercises.....
........................................................................................... 122
5.
Stochastic Gradient Form of Stochastic Approximation
................. 126
5.1
Root-Finding Stochastic Approximation as a Stochastic
Gradient Method
........................................................................... 126
5.1.1
Basic Principles
................................................................. 127
5.1.2
Stochastic Gradient Algorithm
......................................... 131
5.1.3
Implementation in General Nonlinear Regression
Problems
........................................................................... 134
5.1.4
Connection of LMS to Stochastic Gradient
SA................
135
5.2
Neural Network Training.........
..................................................... 138
5.3
Discrete-Event Dynamic Systems.................................................
142
5.4
Image Restoration.........................................................................
144
5.5
Concluding Remarks
......,.............................................................. 147
Exercises.....
........................................................................................... 147
6.
Stochastic Approximation and the Finite-Difference Method
........ 150
6.1
Introduction and Contrast of Gradient-Based and
Gradient-Free Algorithms
............................................................. 150
6.2
Some Motivating Examples for Gradient-Free Stochastic
Approximation.
............................................................................. 153
6.3
Finite-Difference Algorithm
......................................................... 157
6.4
Convergence Theory
..................................................................... 158
6.4.1
Bias in Gradient Estimate
................................................. 158
6.4.2
Convergence
..................................................................... 159
6.5
Asymptotic Normality
................................................................... 162
6.6
Practical Selection of Gain Sequences
........................................, 164
6.7
Several Finite-Difference Examples.............................................
166
6.8
Some Extensions and Enhancements to the Finite· Difference
Algorithm......................................................................................
172
6.9
Concluding Remarks..........
........................................................... 174
Exea.Oises...............
.................................................................................
і
74
7.
Simultaneous Perturbation Stochastic
Approximation ................... 176
7.1
Background.................
.................................................................. 177
7.2
Form and Motivation for Standard SPSA Algorithm
................... 178
7.2.1
Basic Algorithm...
............................................................. 178
7.2.2
Relationship of Gradient Estimate to True Gradient
........ 179
7.3
Basic Assumptions and Supporting Theory for Convergence
...... 182
7.4
Asymptotic Normality and Efficiency Analysis
........................... 186
viii Contents
7.5
Practical
Implementation.............................................................. 188
7.5.1 Step-by-Step Implementation............................................ 188
7.5.2
Choice of Gain Sequences
................................................ 189
7.6
Numerical Examples
..................................................................... 191
7.7
Some Extensions: Optimal Perturbation Distribution;
One-Measurement Form; Global, Discrete, and Constrained
Optimization
................................................................................. 193
7.8
Adaptive SPSA
............................................................................. 196
7.8.1
Introduction and Basic Algorithm
.................................... 196
7.8.2
Implementation Aspects of Adaptive SPSA
..................... 200
7.8.3
Theory on Convergence and Efficiency of Adaptive
SPSA
................................................................................. 201
7.9
Concluding Remarks
..................................................................... 203
7.10
Appendix
:
Conditions for Asymptotic Normality
........................ 204
Exercises
................................................................................................ 204
8.
Annealing-Type Algorithms
................................................................ 208
8.1
Introduction to Simulated Annealing and Motivation from the
Physics of Cooling
........................................................................ 208
8.2
Simulated Annealing Algorithm
................................................... 211
8.2.1
Basic Algorithm
................................................................ 211
8.2.2
Modifications for Noisy Loss Function
Measurements
................................................................... 214
8.3
Some Examples
............................................................................. 217
8.4
Global Optimization via Annealing Algorithms Based on
Stochastic Approximation
............................................................ 221
8.5
Concluding Remarks...
.................................................................. 225
8.6
Appendix: Convergence Theory for Simulated Annealing
Based on Stochastic Approximation
............................................. 226
Exercises
...................................„............................................................ 228
9.
Evolutionary Computation I: Genetic Algorithms
........................... 231
9.1
Introduction
................................................................................... 231
9.2
Some Historical Perspective and Motivating Applications
.......... 235
9.2.1
Brief History
..................................................................... 235
9.2.2
Early Motivation.....
.......................................................... 236
9.3
Coding of Elements for Searching
................................................ 237
9.3.1
Introduction
....................................................................... 237
9.3.2
Standard Bit Coding.....
..................................................... 237
9.3.3
Gray Coding
...................................................................... 240
9.3.4
Real-Number Coding
........................................................ 241
9.4
Standard Genetic Algorithm Operations
....................................... 242
9.4.1
Selection and Elitism
........................................................ 242
CONTENTS
ІХ
9.4.2
Crossover
.......................................................................... 244
9.4.3 Mutation
and Termination
................................................ 245
9.5
Overview of Basic GA Search Approach
..................................... 246
9.6
Practical Guidance and Extensions: Coefficient Values,
Constraints, Noisy Fitness Evaluations, Local Search, and
Parent Selection
............................................................................ 247
9.7
Examples
....................................................................................... 250
9.8
Concluding Remarks....
................................................................. 255
Exercises
................................................................................................ 256
10.
Evolutionary Computation II: General Methods and Theory
........ 259
10.1
Introduction
................................................................................... 259
10.2
Overview of Evolution Strategy and Evolutionary
Programming with Comparisons to Genetic Algorithms
............. 260
10.3
Schema Theory
............................................................................. 263
10.4
What Makes a Problem Hard?
...................................................... 266
10.5
Convergence Theory...
.................................................................. 268
10.6
No Free Lunch Theorems
............................................................. 273
10.7
Concluding Remarks......
............................................................... 275
Exercises
................................................................................................ 276
11.
Reinforcement Learning via Temporal Differences
......................... 278
11.1
Introduction
................................................................................... 278
11.2
Delayed Reinforcement and Formulation for Temporal
Difference Learning
...................................................................... 280
11.3
Basic Temporal Difference Algorithm
......................................... 283
11.4
Batch and Online Implementations of TD Learning
..................... 287
11.5
Some Examples
............................................................................. 289
11.6
Connections to Stochastic Approximation
................................... 295
11.7
Concluding Remarks.............
........................................................ 297
Exercises
..................„............................................................................. 298
12.
Statistical Methods for Optimization in Discrete Problems
............ 300
12.1
Introduction to Multiple Comparisons Over a Finite Set
............. 301
12.2
Statistical Comparisons Test Without Prior Information
..,...,....,, 306
12.3
Multiple Comparisons Against One Candidate with Known
Noise Variance^)
......................................................................... 310
12.4
Multiple Comparisons Against One Candidate with Unknown
Noise Variance(s)
......................................................................... 319
12.5
Extensions to Bonferroni Inequality; Ranking and Selection
Methods in Optimization Over a Finite Set....
.............................. 322
x
Contents
12.6
Concluding Remarks
..................................................................... 325
Exercises
................................................................................................ 326
13.
Model Selection and Statistical Information
..................................... 329
13.1
Bias-Variance Tradeoff
................................................................ 330
13.1.1
Bias and Variance as Contributors to Model
Prediction Error
................................................................. 330
13.1.2
Interpretation of the Bias-Variance Tradeoff
.................. 334
13.1.3
Bias-Variance Analysis for Linear Models
..................... 337
13.2
Model Selection: Cross-Validation
............................................... 340
13.3
The Information Matrix: Applications and Resampling-Based
Computation
................................................................................. 349
13.3.1
Introduction
....................................................................... 349
13.3.2
Fisher Information Matrix: Definition and Two
Equivalent Forms
.............................................................. 350
13.3.3
Two Key Properties of the Information Matrix:
Connections to the Covariance Matrix of Parameter
Estimates
........................................................................... 356
13.3.4
Selected Applications
....................................................... 357
13.3.5
Resampling-Based Calculation of the Information
Matrix
................................................................................ 360
13.4
Concluding Remarks
..................................................................... 363
Exercises
................................................................................................ 364
14.
Simulation-Based Optimization I: Regeneration, Common
Random Numbers, and Selection Methods
....................................... 367
14.1
Background
................................................................................... 367
14.1.1
Focus of Chapter and Roles of Search and
Optimization in Simulation
............................................... 367
14.1.2
Statement of the Optimization Problem
............................ 370
14.2
Regenerative Systems
................................................................... 372
14.2.1
Background and Definition of the Loss Function
£(θ)
..... 372
14.2.2
Estimators of
¿(Θ)
............................................................. 375
14.2.3
Estimates Related to the Gradient of
Ζ(θ)
........................ 380
14.3
Optimization with Finite-Difference and Simultaneous
Perturbation Gradient Estimators
................................................. 382
14.4
Common Random Numbers
.......................................................... 385
14.4.1
Introduction
....................................................................... 385
14.4.2
Theory and Examples for Common Random Numbers
.... 387
14.4.3
Partial Common Random Numbers for Finite Samples....
396
14.5
Selection Methods for Optimization with Discrete-Valued
θ
...... 398
14.6
Concluding Remarks
..................................................................... 405
Exercises
...................................,......................................................... 406
Contents xi
15.
Simulation-Based Optimization
Π:
Stochastic Gradient and Sample
Path Methods
........................................................................................ 409
15.1
Framework for Gradient Estimation
............................................. 409
15.1.1
Some Issues in Gradient Estimation
................................. 409
15.1.2
Gradient Estimation and the Interchange of Derivative
and Integral
....................................................................... 412
15.2
Pure Likelihood Ratio/Score Function and Pure
Infinitesimal Perturbation Analysis
.............................................. 417
15.3
Gradient Estimation Methods in Root-Finding Stochastic
Approximation: The Hybrid LR/SF and
IPA
Setting
................... 420
15.4
Sample Path Optimization
..............................................,............. 425
15.5
Concluding Remarks.............
........................................................ 432
Exercises.......
......................................................................................... 433
16.
Markov Chain Monte Carlo
............................................................... 436
16.1
Background.........
.......................................................................... 436
16.2
Metropolis-Hastings Algorithm...................................................
440
16.3
Gibbs Sampling.....
........................................................................ 445
16.4
Sketch of Theoretical Foundation for Gibbs Sampling
................ 450
16.5
Some Examples of Gibbs Sampling
.............................................. 453
16.6
Applications inBayesian Analysis............
................................... 457
16.7
Concluding Remarks
..................................................................... 461
Exercises....
............................................................................................ 462
17.
Optimal Design for Experimental Inputs
.......................................... 464
17.1
Introduction
................................................................................... 464
17.1.1
Motivation..
....................................................................... 464
17.1.2
Finite-Sample and Asymptotic (Continuous) Designs
..... 469
17.1.3
Precision Matrix and£)-Optimality
.................................. 471
17.2
Linear Models
............................................................................... 473
17.2.1
Background and Connections to Z)-Optimality
................. 473
17.2.2
Some Properties of Asymptotic Designs
.......................... 477
17.2.3
Orthogonal Designs
.......................................................... 481
17.2.4
Sketch of Algorithms for Finding Optimal Designs,....,...
485
17.3
Response Surface Methodology
................................................... 486
17.4
NodinearModels
......................................................................... 489
17.4.1
Introduction.......................................................................
489
17.4.2
Methods for Coping with Dependence on
θ.....................
492
17.5
Concluding Remarks..
................................................................... 500
17.6
Appendix: Optimal Design in Dynamic Models
.......................... 501
Exercises
................................................................................................ 502
xii Contents
Appendix
A. Selected Results from Multivariate Analysis
...................... 505
A.I Multivariate Calculus and Analysis
.............................................. 505
A.2 Some Useful Results in Matrix Theory
........................................ 511
Exercises
................................................................................................ 514
Appendix B. Some Basic Tests in Statistics
............................................... 515
B.I Standard One-Sample Test
........................................................... 515
B.2 Some Basic Two-Sample Tests
.................................................... 518
B.3 Comments on Other Aspects of Statistical Testing
...................... 524
Exercises
................................................................................................ 525
Appendix C. Probability Theory and Convergence
.................................. 526
C.I Basic Properties
............................................................................ 526
C.2 Convergence Theory....
................................................................. 529
C.2.1 Definitions of Convergence
.............................................. 529
C.2.2 Examples and Counterexamples Related to
Convergence
..................................................................... 532
C.2.3 Dominated Convergence Theorem
................................... 534
C.2.4 Convergence in Distribution and Central
Limit Theorem
.................................................................. 535
Exercises
................................................................................................ 537
Appendix D. Random Number Generation
............................................... 538
D.I Background and Introduction to Linear Congruential
Generators
..................................................................................... 538
D
.2
Transformation of Uniform Random Numbers to Other
Distributions
................................................................................. 542
Exercises
................................................................................................ 545
Appendix E. Markov Processes
.................................................................. 547
E.I Background on Markov Processes
................................................ 547
E.2 Discrete Markov Chains
............................................................... 548
Exercises
................................................................................................ 551
Answers to Selected Exercises
..................................................................... 552
References
.....................................................................................................„ 558
Frequently Used Notation
.............................................................,.............. 580
Index
............................................................................................................... 583
|
| any_adam_object | 1 |
| author | Spall, James C. |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV014807577 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:07:24Z |
| institution | BVB |
| isbn | 0471330523 |
| language | English |
| lccn | 2002038049 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010019662 |
| oclc_num | 50773216 |
| open_access_boolean | |
| owner | DE-1051 DE-384 DE-11 DE-355 DE-BY-UBR DE-739 |
| owner_facet | DE-1051 DE-384 DE-11 DE-355 DE-BY-UBR DE-739 |
| physical | xx, 595 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Wiley-Interscience |
| record_format | marc |
| series2 | Wiley-Interscience series in discrete mathematics and optimization |
| spelling | Spall, James C. Verfasser aut Introduction to stochastic search and optimization estimation, simulation, and control James C. Spall Hoboken, NJ Wiley-Interscience 2003 xx, 595 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley-Interscience series in discrete mathematics and optimization Includes bibliographical references (p. 558-579) and index Décision, Théorie de la Optimaliseren gtt Optimisation mathématique Processus stochastiques Stochastische processen gtt Mathematical optimization Search theory Stochastic processes Stochastik (DE-588)4121729-9 gnd rswk-swf Stochastische Optimierung (DE-588)4057625-5 gnd rswk-swf Stochastische Optimierung (DE-588)4057625-5 s DE-604 Stochastik (DE-588)4121729-9 s 1\p DE-604 http://www3.interscience.wiley.com/cgi-bin/booktext/109869022/BOOKPDFSTART Inhaltsverzeichnis http://www.loc.gov/catdir/description/wiley034/2002038049.html Publisher description http://www.loc.gov/catdir/toc/wiley031/2002038049.html Table of contents Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010019662&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Spall, James C. Introduction to stochastic search and optimization estimation, simulation, and control Décision, Théorie de la Optimaliseren gtt Optimisation mathématique Processus stochastiques Stochastische processen gtt Mathematical optimization Search theory Stochastic processes Stochastik (DE-588)4121729-9 gnd Stochastische Optimierung (DE-588)4057625-5 gnd |
| subject_GND | (DE-588)4121729-9 (DE-588)4057625-5 |
| title | Introduction to stochastic search and optimization estimation, simulation, and control |
| title_auth | Introduction to stochastic search and optimization estimation, simulation, and control |
| title_exact_search | Introduction to stochastic search and optimization estimation, simulation, and control |
| title_full | Introduction to stochastic search and optimization estimation, simulation, and control James C. Spall |
| title_fullStr | Introduction to stochastic search and optimization estimation, simulation, and control James C. Spall |
| title_full_unstemmed | Introduction to stochastic search and optimization estimation, simulation, and control James C. Spall |
| title_short | Introduction to stochastic search and optimization |
| title_sort | introduction to stochastic search and optimization estimation simulation and control |
| title_sub | estimation, simulation, and control |
| topic | Décision, Théorie de la Optimaliseren gtt Optimisation mathématique Processus stochastiques Stochastische processen gtt Mathematical optimization Search theory Stochastic processes Stochastik (DE-588)4121729-9 gnd Stochastische Optimierung (DE-588)4057625-5 gnd |
| topic_facet | Décision, Théorie de la Optimaliseren Optimisation mathématique Processus stochastiques Stochastische processen Mathematical optimization Search theory Stochastic processes Stochastik Stochastische Optimierung |
| url | http://www3.interscience.wiley.com/cgi-bin/booktext/109869022/BOOKPDFSTART http://www.loc.gov/catdir/description/wiley034/2002038049.html http://www.loc.gov/catdir/toc/wiley031/2002038049.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010019662&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT spalljamesc introductiontostochasticsearchandoptimizationestimationsimulationandcontrol |
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