Multilevel methods for dynamic programming: deterministic and stochastic iterative methods with application to recommendation engines
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
München
AVM
2011
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| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XIII, 111 S. graph. Darst. 21 cm |
| ISBN: | 9783869241722 |
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Record in the Search Index
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IMAGE 1
CONTENTS
LIST OF FIGURES V
LIST OF TABLES VII
LIST OF ALGORITHMS BE
LIST OF SYMBOLS XI
CHAPTER 1. PREFACE 1
1.1. INTRODUCTION 1
1.2. OUTLINE 4
CHAPTER 2. PRELIMINARIES 7
2.1. INTRODUCTORY REMARKS 7
2.2. MARKOV PROCESSES AND OPTIMAL CONTROL 7
2.3. BACKGROUND IN MATRIX THEORY 10
2.3.1. INTRODUCTORY REMARKS 10
2.3.2. NONNEGATIVE MATRICES 11
2.3.3. STOCHASTIC MATRICES 14
2.3.4. SUBSTOCHASTIC MATRICES 17
2.3.5. STABLE MATRICES 19
2.4. ITERATIVE METHODS FOR SYSTEMS OF LINEAR EQUATIONS 19
2.4.1. INTRODUCTORY REMARKS 19
2.4.2. SPLITTING THEORY 20
2.4.3. ALGEBRAIC MULTIGRID AND CORRECTION METHODS 23
2.5. DYNAMIC PROGRAMMING 26
2.5.1. BELLMAN EQUATIONS 26
2.5.2. DISCOUNTED PROBLEMS 27
2.5.3. STOCHASTIC SHORTEST PATH PROBLEMS 31
2.5.4. ON THE RELATION BETWEEN DISCOUNTED, STOCHASTIC SHORTEST PATH AND
AVERAGE COST PER STAGE PROBLEMS 34
2.6. STOCHASTIC ITERATIVE DYNAMIC PROGRAMMING 36
2.6.1. INTRODUCTORY REMARKS 36
2.6.2. NOTATION AND AGREEMENTS 38
2.6.3. MODEL-BASED METHODS 39
2.6.4. MONTE CARLO POLICY EVALUATION 42
2.6.5. TD(A) FOR DISCOUNTED PROBLEMS 42
2.6.6. TD(A) FOR STOCHASTIC SHORTEST PATH PROBLEMS 46
2.6.7. REMARKS ON CONVERGENCE RATES 47
CHAPTER 3. DETERMINISTIC METHODS 49
3.1. INTRODUCTORY REMARKS 49
3.2. PERTURBATION ANALYSIS 49
3.2.1. MOTIVATION AND PRELIMINARIES 49
3.2.2. DISCOUNTED PROBLEMS 50
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1017746028
DIGITALISIERT DURCH
IMAGE 2
3.2.3. STOCHASTIC SHORTEST PATH PROBLEMS 51
3.3. BASIC METHODS WITH SUBDOMINANT CONVERGENCE RATE 52
3.3.1. COMPARISON OF DIFFERENT SPLITTINGS 52
3.3.2. DEFLATION AND EXTRAPOLATION METHODS 53
3.4. LUMPABILITY AND APPROXIMATE LUMPABILITY 54
3.5. NEARLY COMPLETE DECOMPOSABILITY AND WEAK COUPLING 59
3.6. ABSTRACT RESULTS ON MULTILEVEL METHODS FOR NON-SYMMETRIC SYSTEMS 61
3.7. ALGEBRAIC MULTIGRID WITH STATE AGGREGATION 68
3.7.1. ALGORITHM PRESENTATION 68
3.7.2. CONVERGENCE RESULTS 69
3.8. ALGEBRAIC SCHWARZ METHODS 75
3.9. ITERATIVE AGGREGATION-DISAGGREGATION 79
CHAPTER 4. STOCHASTIC ITERATIVE METHODS 83
4.1. INTRODUCTORY REMARKS 83
4.2. THE LB-MGTD(A) AND S-MGTD(A) ALGORITHMS FOR DISCOUNTED PROBLEMS 83
4.2.1. PRELIMINARIES 83
4.2.2. LEVEL-BASED MULTIGRID TD(A) 84
4.2.3. SIMULTANEOUS MULTIGRID TD(A) 85
4.3. GENERALIZATION TO STOCHASTIC SHORTEST PATH PROBLEMS 86
4.3.1. LB-MGTD(A) 86
4.3.2. SMGTD(A) 86
CHAPTER 5. NUMERICAL RESULTS 89
5.1. PRELIMINARIES 89
5.2. THE MODEL PROBLEMS 89
5.3. DETERMINISTIC METHODS 92
5.3.1. COMPARISON OF SPECTRAL RADII 92
5.3.2. COMPARISON OF RUNTIMES 94
5.3.3. CONCLUDING REMARKS 96
5.4. STOCHASTIC ITERATIVE METHODS 97
5.4.1. INTRODUCTORY REMARKS 97
5.4.2. EXPERIMENT DESCRIPTION 98
5.4.3. DISCOUNTED PROBLEMS 98
5.4.4. STOCHASTIC SHORTEST PATH PROBLEMS 101
5.4.5. CONCLUDING REMARKS 103
CHAPTER 6. CONCLUSIONS AND OUTLOOK 105
BIBLIOGRAPHY 107 |
| any_adam_object | 1 |
| author | Paprotny, Alexander |
| author_GND | (DE-588)1018069577 |
| author_facet | Paprotny, Alexander |
| author_role | aut |
| author_sort | Paprotny, Alexander |
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| building | Verbundindex |
| bvnumber | BV039778808 |
| classification_tum | MAT 917 |
| ctrlnum | (OCoLC)772978669 (DE-599)DNB1017746028 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV039778808 |
| illustrated | Illustrated |
| indexdate | 2024-07-21T00:19:29Z |
| institution | BVB |
| isbn | 9783869241722 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024639671 |
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| owner_facet | DE-12 DE-91G DE-BY-TUM |
| physical | XIII, 111 S. graph. Darst. 21 cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | AVM |
| record_format | marc |
| spelling | Paprotny, Alexander Verfasser (DE-588)1018069577 aut Multilevel methods for dynamic programming deterministic and stochastic iterative methods with application to recommendation engines Alexander Paprotny München AVM 2011 XIII, 111 S. graph. Darst. 21 cm txt rdacontent n rdamedia nc rdacarrier Literaturangaben Iteration (DE-588)4123457-1 gnd rswk-swf Lineares Gleichungssystem (DE-588)4035826-4 gnd rswk-swf Dynamische Optimierung (DE-588)4125677-3 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 gnd rswk-swf Empfehlungssystem (DE-588)7511891-9 gnd rswk-swf Optimale Kontrolle (DE-588)4121428-6 s Lineares Gleichungssystem (DE-588)4035826-4 s Iteration (DE-588)4123457-1 s Dynamische Optimierung (DE-588)4125677-3 s Empfehlungssystem (DE-588)7511891-9 s DE-604 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3930994&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024639671&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Paprotny, Alexander Multilevel methods for dynamic programming deterministic and stochastic iterative methods with application to recommendation engines Iteration (DE-588)4123457-1 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd Dynamische Optimierung (DE-588)4125677-3 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Empfehlungssystem (DE-588)7511891-9 gnd |
| subject_GND | (DE-588)4123457-1 (DE-588)4035826-4 (DE-588)4125677-3 (DE-588)4121428-6 (DE-588)7511891-9 |
| title | Multilevel methods for dynamic programming deterministic and stochastic iterative methods with application to recommendation engines |
| title_auth | Multilevel methods for dynamic programming deterministic and stochastic iterative methods with application to recommendation engines |
| title_exact_search | Multilevel methods for dynamic programming deterministic and stochastic iterative methods with application to recommendation engines |
| title_full | Multilevel methods for dynamic programming deterministic and stochastic iterative methods with application to recommendation engines Alexander Paprotny |
| title_fullStr | Multilevel methods for dynamic programming deterministic and stochastic iterative methods with application to recommendation engines Alexander Paprotny |
| title_full_unstemmed | Multilevel methods for dynamic programming deterministic and stochastic iterative methods with application to recommendation engines Alexander Paprotny |
| title_short | Multilevel methods for dynamic programming |
| title_sort | multilevel methods for dynamic programming deterministic and stochastic iterative methods with application to recommendation engines |
| title_sub | deterministic and stochastic iterative methods with application to recommendation engines |
| topic | Iteration (DE-588)4123457-1 gnd Lineares Gleichungssystem (DE-588)4035826-4 gnd Dynamische Optimierung (DE-588)4125677-3 gnd Optimale Kontrolle (DE-588)4121428-6 gnd Empfehlungssystem (DE-588)7511891-9 gnd |
| topic_facet | Iteration Lineares Gleichungssystem Dynamische Optimierung Optimale Kontrolle Empfehlungssystem |
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