Stochastic recursive algorithms for optimization: simultaneous perturbation methods
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2013
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| Series: | Lecture notes in control and information sciences
434 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 302 S. graph. Darst. |
| ISBN: | 9781447142843 |
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| LEADER | 00000nam a2200000 cb4500 | ||
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| 003 | DE-604 | ||
| 005 | 20131007 | ||
| 007 | t | ||
| 008 | 121008s2013 d||| |||| 00||| eng d | ||
| 020 | |a 9781447142843 |9 978-1-4471-4284-3 | ||
| 035 | |a (OCoLC)812338703 | ||
| 035 | |a (DE-599)BSZ370684532 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-83 |a DE-824 |a DE-355 | ||
| 084 | |a SI 845 |0 (DE-625)143198: |2 rvk | ||
| 100 | 1 | |a Bhatnagar, Shalabh |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Stochastic recursive algorithms for optimization |b simultaneous perturbation methods |c S. Bhatnagar, H. L. Prasad, and L. A. Prashanth |
| 264 | 1 | |a London [u.a.] |b Springer |c 2013 | |
| 300 | |a XVI, 302 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in control and information sciences |v 434 | |
| 650 | 4 | |a Ingenieurwissenschaften | |
| 650 | 4 | |a Engineering | |
| 650 | 4 | |a Systems theory | |
| 650 | 4 | |a Mathematical optimization | |
| 700 | 1 | |a Prasad, H. L. |e Verfasser |4 aut | |
| 700 | 1 | |a Prashanth, L. A. |e Verfasser |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4471-4285-0 |
| 830 | 0 | |a Lecture notes in control and information sciences |v 434 |w (DE-604)BV005848579 |9 434 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025306308&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025306308 | ||
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| _version_ | 1804149522958385152 |
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| adam_text | Contents
Part I Introduction to Stochastic Recursive Algorithms
1
Introduction
................................................... 3
1.
1 Introduction
............................................... 3
1.2
Overview of the Remaining Chapters
.......................... 7
1.3
Concluding Remarks
........................................
J
1
References
..................................................... 11
2
Deterministic Algorithms for LocaJ Search
........................ 13
2.1
Introduction
............................................... 13
2.2
Deterministic Algorithms for Local Search
..................... 14
References
..................................................... 15
3
Stochastic Approximation Algorithms
............................. 17
3.1
Introduction
............................................... 17
3.2
The Robbins-Monro Algorithm
............................... 18
3.2.1
Convergence of the Robbms-Monro Algorithm
........... 19
3.3
Multi-timescale Stochastic Approximation
...................... 23
3.3
Л
Convergence of the Multi-timescale Algorithm
........... 24
3.4
Concluding Remarks
......................................... 26
References
...................................................... 27
Part II Gradient Estimation Schemes
4 Kiefer-Wolfowitz
Algorithm
..................................... 31
4.1
Introduction
............................................... 31
4.2
The Basic Algorithm
......................................... 31
4.2.1
Extension to Multi-dimensionaJ Parameter
............... 35
4.3
Variants of the
Kiefer-Wolfowitz.
Algorithm
.................... 36
4.3.1
Fixed Perturbation Parameter
.......................... 36
4.3.2
One-Sided Variants
................................... 37
XII Contents
4.4
Concluding Remarks
........................................ 38
References
..................................................... 38
5
Gradient Schemes with Simultaneous Perturbation Stochastic
Approximation
................................................. 41
5.1
Introduction
............................................... 41
5.2
The Basic SPSA Algorithm
.................................. 41
5.2.1
Gradient Estimate Using Simultaneous Perturbation
....... 42
5.2.2
The Algorithm
...................................... 43
5.2.3
Convergence Analysis
................................ 44
5.3
Variants of the Basic SPSA Algorithm
.......................... 47
5.3.1
One-Measurement SPSA Algorithm
.................... 47
5.3.2
One-Sided SPSA Algorithm
........................... 49
5.3.3
Fixed Perturbation Parameter
.......................... 49
5.4
General Remarks on SPSA Algorithms
........................ 51
5.5
SPSA Algorithms with Deterministic Perturbations
.............. 52
5.5.1
Properties of Deterministic Perturbation Sequences
........ 52
5.5.2
Hadamard
Matrix Based Construction
................... 54
5.5.3
Two-Sided SPSA with
Hadamard
Matrix Perturbations
.... 56
5.5.4
One-Sided SPSA with
Hadamard
Matrix Perturbations
..... 62
5.5.5
One-Measurement SPSA with
Hadamard
Matrix
Perturbations
........................................ 63
5.6
SPSA Algorithms for Long-Run Average Cost Objective
......... 65
5.6.
J
The Framework
...................................... 65
5.6.2
The Two-Simulation SPSA Algorithm
.................... 65
5.6.3
Assumptions
........................................ 66
5.6.4
Convergence Analysis
................................ 68
5.6.5
Projected SPSA Algorithm
............................ 73
5.7
Concluding Remarks
........................................ 75
References
..................................................... 75
6
Smoothed Functional Gradient Schemes
.......................... 77
6.1
Introduction
............................................... 77
6.2
Gaussian Based SF Algorithm
................................ 79
6.2.1
Gradient Estimation via Smoothing
..................... 79
6.2.2
The Basic Gaussian SF Algorithm
...................... 81
6.2.3
Convergence Analysis of Gaussian SF Algorithm
......... 82
6.2.4
Two-Measurement Gaussian SF Algorithm
............... 88
6.3
General Conditions for a Candidate Smoothing Function
.......... 91
6.4
Cauchy Variant of the SF Algorithm
........................... 92
6.4.1
Gradient Estimate
.................................... 92
6.4.2
Cauchy SF Algorithm
................................ 94
6.5
SF Algorithms for the Long-Run Average Cost Objective
......... 94
6.5.1
The G-SF1 Algorithm
................................ 95
6.5.2
The G-SF2 Algorithm
................................ 99
Contents XIII
6.5.3
Projected
SF
Algorithms
..............................100
6.6
Concluding Remarks
........................................101
References
.....................................................101
Part III Hessian Estimation Schemes
7
Newton-Based Simultaneous Perturbation Stochastic Approximation
105
7.1
Introduction
...............................................105
7.2
The Framework
............................................106
7.3
Newton SPSA Algorithms
...................................106
7.3.1
Four-Simulation.Newton SPSA (N-SPSA4)
..............107
7.3.2
Three-Simulation Newton SPSA
(N-SPSA3)
.............109
7.3.3
Two-Simulation Newton SPSA (N-SPSA2)
..............110
7.3.4
One-Simulation Newton SPSA (N-SPSA1)
..............
Ill
7.4
Woodbury s Identity Based Newton SPSA Algorithms
...........113
7.5
Convergence Analysis
.......................................114
7.5.1
Assumptions
........................................114
7.5.2
Convergence Analysis of N-SPSA4
.....................117
7.5.3
Convergence Analysis of N-SPSA3
.....................125
7.5.4
Convergence Analysis of N-SPSA2
.....................126
7.5.5
Convergence Analysis of N-SPSA1
.....................128
7.5.6
Convergence Analysis of W-SPSA Algorithms
...........130
7.6
Concluding Remarks
........................................130
References
.....................................................131
8
Newton-Based Smoothed FunctionaJ Algorithms
...................133
8.1
Introduction
................................................133
8.2
The Hessian Estimates
......................................134
8.2.1
One-Simulation Hessian SF Estimate
...................134
8.2.2
Two-Simulation Hessian SF Estimate
...................136
8.3
The Newton SF Algorithms
..................................137
8.3.1
The One-Simulation Newton SF Algorithm (N-SF1)
.......137
8.3.2
The Two-Simulation Newton SF Algorithm (N-SF2)
.......138
8.4
Convergence Analysis of Newton SF Algorithms
................139
8.4.1
Convergence of N-SF1
................................ 139
8.4.2
Convergence of N-SF2
.................................146
8.5
Concluding Remarks
.........................................147
References
.....................................................147
Part IV Variations to the Basic Scheme
9
Discrete Parameter Optimization
................................151
9.1
Introduction
...............................................151
9.2
The Framework
............................................152
9.2.1
The Deterministic Projection Operator
..................153
9.2.2
The Random Projection Operator
.......................154
XIV Contents
9.2.3
A Generalized Projection Operator
.....................155
9.2.4
Regular Projection Operator to
Č
.......................1 57
9.2.5
Basic Results for the Generalized Projection Operator Case
. 157
9.3
The Algorithms
............................................160
9.3.1
The SPSA Algorithm
.................................160
9.3.2
The
SFA
Algorithm
..................................161
9.3.3
Convergence Analysis
................................162
9.4
Concluding Remarks
........................................164
References
.....................................................166
10
Algorithms for Constrained Optimization
.........................167
10.1
Introduction
...............................................167
10.2
The Framework
............................................168
10.3
Algorithms
................................................171
10.3.1
Constrained Gradient-Based SPSA Algorithm
(CG-
SPSA)
.172
10.3.2
Constrained Newton-Based SPSA Algorithm (CN-SPSA)
..173
10.3.3
Constrained Gradient-Based SF Algorithm (CG-SF)
.......175
10.3.4
Constrained Newton-Based SF Algorithm (CN-SF)
........176
10.4
A Sketch of the Convergence
.................................178
10.5
Concluding Remarks
........................................185
References
.....................................................1 86
11
Reinforcement Learning
........................................1 87
11.1
Introductjon
...............................................1 87
11.2
Markov Decision Processes
..................................188
11.3
Numerical Procedures for MDPs
..............................191
11.3.1
Numerical Procedures for Discounted Cost MDPs
.........192
11.3.2
Numerical Procedures for Long Run Average Cost MDPs
.193
11.4
Reinforcement Learning Algorithms for Look-up Table Case
......194
11.4.1
An Actor-Critic Algorithm for Infinite Horizon Discounted
Cost MDPs
.........................................195
11.4.2
The Q-Learning Algorithm and a Simultaneous
Perturbation Variant for Infinite Horizon Discounted Cost
MDPs
..............................................198
11.4.3
Actor Critic Algorithms for Long-Run Average Cost MDPs
202
11.5
Reinforcement Learning Algorithms with Function Approximation
. 206
11.5.1
Temporal Difference (TD) Learning with Discounted Cost.
. 206
11.5.2
An Actor-Critic Algorithm with a Temporal Difference
Critic for Discounted Cost MDPs
.......................210
11.5.3
Function Approximation Based Q-learning Algorithm and
a Simultaneous Perturbation Variant for Infinite Horizon
Discounted Cost MDPs
...............................213
11.6
Concluding Remarks
........................................218
References
.....................................................218
Contenes
XV
Part V
Applications
12
Service Systems
................................................225
12.1
Introduction
...............................................225
12.2
Service System
Framework
..................................226
12.3
Problem
Formulation
.......................................228
12.4
Solution Methodology
......................................232
12.5
First Order Methods
........................................234
12.5.1
SASOC-SPSA
......................................234
12.5.2
SASOC-SF-N
.......................................235
1 2.5.3
SASOC-SF-C
.......................................236
12.6
Second Order Methods
......................................236
12.6.1
SASOC-H
..........................................237
12.6.2
SASOC-W
..........................................237
12.7
Notes on Convergence
......................................238
12.8
Summary of Experiments
....................................239
12.9
Concluding Remarks
........................................240
References
.....................................................240
13
Road Traffic Control
243
13.1
Introduction
...............................................243
1 3.2
Q-Learning for Traffic Light Control
..........................245
1 3.2. ]
Traffic Control Problem as an MDP
.....................245
13.2.2
The
TLC
Algorithm
..................................246
13.2.3
Summary of Experimental Results
......................248
13.3
Threshold Tuning Using SPSA
...............................248
13.3.1
The Threshold Tuning Algorithm
.......................249
13.3.2
Traffic Light Control with Threshold Tuning
.............250
13.3.3
Summary of Experimental Results
......................254
13.4
Concluding Remarks
........................................255
References
.....................................................255
14
Communication Networks
.......................................257
14.1
Introduction
................................................257
14.2
The Random Early Detection (RED) Scheme for the Internet
......258
14.2.1
Introduction to RED Flow Control
......................258
14.2.2
The Framework
......................................259
14.2.3
The
В
RED and
Ρ
RED Stochastic Approximation
Algorithms
.........................................263
14.2.4
Summary of Experimental Results
......................266
14.3
Optimal Policies for the Retransmission Probabilities in Slotted
Aloha
....................................................267
14.3.1
Introduction to the Slotted Aloha Multiaccess
Communication Protocol
..............................267
14.3.2
The SDE Framework
.................................268
XVI Contents
14.3.3
The Algorithm
......................................270
14.3.4
Summary of Experimental Results
......................272
14.4
Dynamic Multi-layered Pricing Schemes for the Internet
..........272
14.4.1
Introduction to Dynamic Pricing Schemes
...............273
14.4.2
The Pricing Framework
...............................273
14.4.3
The
Pnce
Feed-Back Policies and the Algorithms
.........275
14.4.4
Summary of Experimental Results
......................277
14.5
Concluding Remarks
........................................278
References
.....................................................279
Part VI Appendix
A Convergence Notions for a Sequence of Random Vectors
............283
Reference
......................................................285
В
Martingales
...................................................287
References
.....................................................289
С
Ordinary Differential Equations
.................................291
References
......................................................294
D
The Borkar-Meyn Theorem for Stability and Convergence of
Stochastic Approximation
.......................................295
References
.....................................................296
E
The Kushner-Clark Theorem for Convergence of Projected
Stochastic Approximation
.......................................297
References
.....................................................300
Index
.............................................................301
|
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| id | DE-604.BV040458813 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:24:22Z |
| institution | BVB |
| isbn | 9781447142843 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025306308 |
| oclc_num | 812338703 |
| open_access_boolean | |
| owner | DE-83 DE-824 DE-355 DE-BY-UBR |
| owner_facet | DE-83 DE-824 DE-355 DE-BY-UBR |
| physical | XVI, 302 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in control and information sciences |
| series2 | Lecture notes in control and information sciences |
| spelling | Bhatnagar, Shalabh Verfasser aut Stochastic recursive algorithms for optimization simultaneous perturbation methods S. Bhatnagar, H. L. Prasad, and L. A. Prashanth London [u.a.] Springer 2013 XVI, 302 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in control and information sciences 434 Ingenieurwissenschaften Engineering Systems theory Mathematical optimization Prasad, H. L. Verfasser aut Prashanth, L. A. Verfasser aut Erscheint auch als Online-Ausgabe 978-1-4471-4285-0 Lecture notes in control and information sciences 434 (DE-604)BV005848579 434 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025306308&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bhatnagar, Shalabh Prasad, H. L. Prashanth, L. A. Stochastic recursive algorithms for optimization simultaneous perturbation methods Lecture notes in control and information sciences Ingenieurwissenschaften Engineering Systems theory Mathematical optimization |
| title | Stochastic recursive algorithms for optimization simultaneous perturbation methods |
| title_auth | Stochastic recursive algorithms for optimization simultaneous perturbation methods |
| title_exact_search | Stochastic recursive algorithms for optimization simultaneous perturbation methods |
| title_full | Stochastic recursive algorithms for optimization simultaneous perturbation methods S. Bhatnagar, H. L. Prasad, and L. A. Prashanth |
| title_fullStr | Stochastic recursive algorithms for optimization simultaneous perturbation methods S. Bhatnagar, H. L. Prasad, and L. A. Prashanth |
| title_full_unstemmed | Stochastic recursive algorithms for optimization simultaneous perturbation methods S. Bhatnagar, H. L. Prasad, and L. A. Prashanth |
| title_short | Stochastic recursive algorithms for optimization |
| title_sort | stochastic recursive algorithms for optimization simultaneous perturbation methods |
| title_sub | simultaneous perturbation methods |
| topic | Ingenieurwissenschaften Engineering Systems theory Mathematical optimization |
| topic_facet | Ingenieurwissenschaften Engineering Systems theory Mathematical optimization |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025306308&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005848579 |
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