Stochastic approximation: a dynamical systems viewpoint
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press [u.a.]
2008
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Incl. bibliogr. references and index |
| Beschreibung: | IX, 164 S. |
| ISBN: | 9780521515924 0521515920 |
Internformat
MARC
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| 100 | 1 | |a Borkar, Vivek S. |d 1954- |e Verfasser |0 (DE-588)171737091 |4 aut | |
| 245 | 1 | 0 | |a Stochastic approximation |b a dynamical systems viewpoint |c Vivek S. Borkar |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press [u.a.] |c 2008 | |
| 300 | |a IX, 164 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Incl. bibliogr. references and index | ||
| 650 | 0 | |a Stochastic approximation | |
| 650 | 4 | |a Approximation stochastique | |
| 650 | 4 | |a Stochastic approximation | |
| 650 | 0 | 7 | |a Stochastische Approximation |0 (DE-588)4183371-5 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016980623 | ||
Datensatz im Suchindex
| _version_ | 1804138343110279168 |
|---|---|
| adam_text | Contents
Preface
,
page vii
1
Introduction
1
2
Basic
Convergence Analysis
10
2.1
The o.d.e. limit
10
2.2
Extensions and variations
16
3
Stability Criteria
21
3.1
Introduction
21
3.2
Stability criterion
21
3.3
Another stability criterion
27
4
Lock-in Probability
31
4.1
Estimating the lock-in probability
31
4.2
Sample complexity
42
4.3
Avoidance of traps
44
5
Stochastic Recursive Inclusions
52
5.1
Preliminaries
52
5.2
The differential inclusion limit
53
5.3
Applications
56
5.4
Projected stochastic approximation
59
6
Multiple Timescales
64
6.1
Two timescales
64
6.2
Averaging the natural timescale: preliminaries
67
6.3
Averaging the natural timescale: main results
73
6.4
Concluding remarks
76
7
Asynchronous Schemes
78
7.1
Introduction
78
7.2
Asymptotic behavior
80
7.3
Effect of delays
82
7.4
Convergence
85
vi
Contents
8
A
Limit Theorem
for Fluctuations
88
8.1
Introduction
88
8.2
A tightness result
89
8.3
The functional central limit theorem
96
8.4
The convergent case
99
9
Constant Stepsize Algorithms
101
9.1
Introduction
101
9.2
Asymptotic behaviour
102
9.3
Refinements
107
10
Applications
117
10.1
Introduction
117
10.2
Stochastic gradient schemes
118
10.3
Stochastic fixed point iterations
125
10.4
Collective phenomena
131
10.5
Miscellaneous applications
137
11
Appendices
140
11.1
Appendix A: Topics in analysis
140
11.1.1
Continuous functions
140
11.1.2
Square-integrable functions
141
11.1.3
Lebesgue s theorem
143
11.2
Appendix B: Ordinary differential equations
143
11.2.1
Basic theory
143
11.2.2
Linear systems
146
11.2.3
Asymptotic behaviour
147
11.3
Appendix C: Topics in probability
149
11.3.1
Martingales
149
11.3.2
Spaces of probability measures
152
11.3.3
Stochastic differential equations
153
References
156
Index
163
|
| adam_txt |
Contents
Preface
,
page vii
1
Introduction
1
2
Basic
Convergence Analysis
10
2.1
The o.d.e. limit
10
2.2
Extensions and variations
16
3
Stability Criteria
21
3.1
Introduction
21
3.2
Stability criterion
21
3.3
Another stability criterion
27
4
Lock-in Probability
31
4.1
Estimating the lock-in probability
31
4.2
Sample complexity
42
4.3
Avoidance of traps
44
5
Stochastic Recursive Inclusions
52
5.1
Preliminaries
52
5.2
The differential inclusion limit
53
5.3
Applications
56
5.4
Projected stochastic approximation
59
6
Multiple Timescales
64
6.1
Two timescales
64
6.2
Averaging the natural timescale: preliminaries
67
6.3
Averaging the natural timescale: main results
73
6.4
Concluding remarks
76
7
Asynchronous Schemes
78
7.1
Introduction
78
7.2
Asymptotic behavior
80
7.3
Effect of delays
82
7.4
Convergence
85
vi
Contents
8
A
Limit Theorem
for Fluctuations
88
8.1
Introduction
88
8.2
A tightness result
89
8.3
The functional central limit theorem
96
8.4
The convergent case
99
9
Constant Stepsize Algorithms
101
9.1
Introduction
101
9.2
Asymptotic behaviour
102
9.3
Refinements
107
10
Applications
117
10.1
Introduction
117
10.2
Stochastic gradient schemes
118
10.3
Stochastic fixed point iterations
125
10.4
Collective phenomena
131
10.5
Miscellaneous applications
137
11
Appendices
140
11.1
Appendix A: Topics in analysis
140
11.1.1
Continuous functions
140
11.1.2
Square-integrable functions
141
11.1.3
Lebesgue's theorem
143
11.2
Appendix B: Ordinary differential equations
143
11.2.1
Basic theory
143
11.2.2
Linear systems
146
11.2.3
Asymptotic behaviour
147
11.3
Appendix C: Topics in probability
149
11.3.1
Martingales
149
11.3.2
Spaces of probability measures
152
11.3.3
Stochastic differential equations
153
References
156
Index
163 |
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| author | Borkar, Vivek S. 1954- |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 1. publ. |
| format | Book |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:55:17Z |
| indexdate | 2024-07-09T21:26:41Z |
| institution | BVB |
| isbn | 9780521515924 0521515920 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016980623 |
| oclc_num | 231580915 |
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| owner | DE-703 DE-824 DE-11 DE-521 DE-384 DE-706 |
| owner_facet | DE-703 DE-824 DE-11 DE-521 DE-384 DE-706 |
| physical | IX, 164 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge Univ. Press [u.a.] |
| record_format | marc |
| spelling | Borkar, Vivek S. 1954- Verfasser (DE-588)171737091 aut Stochastic approximation a dynamical systems viewpoint Vivek S. Borkar 1. publ. Cambridge Cambridge Univ. Press [u.a.] 2008 IX, 164 S. txt rdacontent n rdamedia nc rdacarrier Incl. bibliogr. references and index Stochastic approximation Approximation stochastique Stochastische Approximation (DE-588)4183371-5 gnd rswk-swf Stochastische Approximation (DE-588)4183371-5 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016980623&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Borkar, Vivek S. 1954- Stochastic approximation a dynamical systems viewpoint Stochastic approximation Approximation stochastique Stochastische Approximation (DE-588)4183371-5 gnd |
| subject_GND | (DE-588)4183371-5 |
| title | Stochastic approximation a dynamical systems viewpoint |
| title_auth | Stochastic approximation a dynamical systems viewpoint |
| title_exact_search | Stochastic approximation a dynamical systems viewpoint |
| title_exact_search_txtP | Stochastic approximation a dynamical systems viewpoint |
| title_full | Stochastic approximation a dynamical systems viewpoint Vivek S. Borkar |
| title_fullStr | Stochastic approximation a dynamical systems viewpoint Vivek S. Borkar |
| title_full_unstemmed | Stochastic approximation a dynamical systems viewpoint Vivek S. Borkar |
| title_short | Stochastic approximation |
| title_sort | stochastic approximation a dynamical systems viewpoint |
| title_sub | a dynamical systems viewpoint |
| topic | Stochastic approximation Approximation stochastique Stochastische Approximation (DE-588)4183371-5 gnd |
| topic_facet | Stochastic approximation Approximation stochastique Stochastische Approximation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016980623&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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