Neuro-dynamic programming:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Belmont, Mass.
Athena Scientific
1996
|
| Schriftenreihe: | Athena Scientific optimization and computation series
3 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010098849&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Umfang: | XIII, 491 S. graph. Darst. |
| ISBN: | 1886529108 |
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Datensatz im Suchindex
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|---|---|
| DE-BY-TUM_katkey | 1535245 |
| DE-BY-TUM_location | 00 LSB |
| DE-BY-TUM_media_number | 040006714672 040009431132 040006408911 040020291067 |
| _version_ | 1821932939148001281 |
| adam_text | Contents
1. Introduction p. 1
1.1. Cost to go Approximations in Dynamic Programming .... p. 3
1.2. Approximation Architectures p. 5
1.3. Simulation and Training p. 6
1.4. Neuro Dynamic Programming p. 8
1.5. Notes and Sources p. 9
2. Dynamic Programming p. 11
2.1. Introduction p. 12
2.1.1. Finite Horizon Problems p. 13
2.1.2. Infinite Horizon Problems p. 14
2.2. Stochastic Shortest Path Problems p. 17
2.2.1. General Theory p. 18
2.2.2. Value Iteration p. 25
2.2.3. Policy Iteration p. 29
2.2.4. Linear Programming p. 36
2.3. Discounted Problems p. 37
2.3.1. Temporal Difference Based Policy Iteration p. 41
2.4. Problem Formulation and Examples p. 47
2.5. Notes and Sources p. 57
3. Neural Network Architectures and Training p. 59
3.1. Architectures for Approximation p. 60
3.1.1. An Overview of Approximation Architectures p. 61
3.1.2. Features p. 66
3.1.3. Partitioning p. 70
3.1.4. Using Heuristic Policies to Construct Features . . . . p. 72
3.2. Neural Network Training p. 76
3.2.1. Optimality Conditions p. 78
3.2.2. Linear Least Squares Methods p. 81
3.2.3. Gradient Methods p. 89
v
vi Contents
3.2.4. Incremental Gradient Methods for Least Squares . . p. 108
3.2.5. Convergence Analysis of Incremental Gradient
Methods p. 115
3.2.6. Extended Kalman Filtering p. 124
3.2.7. Comparison of Various Methods p. 128
3.3. Notes and Sources p. 129
4. Stochastic Iterative Algorithms p. 131
4.1. The Basic Model p. 134
4.2. Convergence Based on a Smooth Potential Function .... p. 139
4.2.1. A Convergence Result p. 139
4.2.2. Two Pass Methods p. 147
4.2.3. Convergence Proofs p. 148
4.3. Convergence under Contraction or Monotonicity
Assumptions p. 154
4.3.1. Algorithmic Model p. 154
4.3.2. Weighted Maximum Norm Contractions p. 155
4.3.3. Time Dependent Maps and Additional Noise Terms . p. 157
4.3.4. Convergence under Monotonicity Assumptions ... p. 158
4.3.5. Boundedness p. 159
4.3.6. Convergence Proofs p. 161
4.4. The ODE Approach p. 171
4.4.1. The Case of Markov Noise p. 173
4.5. Notes and Sources p. 178
5. Simulation Methods for a Lookup Table Representation p. 179
5.1. Some Aspects of Monte Carlo Simulation p. 181
5.2. Policy Evaluation by Monte Carlo Simulation p. 186
5.2.1. Multiple Visits to the Same State p. 187
5.2.2. Q Factors and Policy Iteration p. 192
5.3. Temporal Difference Methods p. 193
5.3.1. Monte Carlo Simulation Using Temporal
Differences p. 193
5.3.2. TD(A) p. 195
5.3.3. General Temporal Difference Methods p. 201
5.3.4. Discounted Problems p. 204
5.3.5. Convergence of Off Line Temporal Difference
Methods p. 208
5.3.6. Convergence of On Line Temporal Difference
Methods p. 219
5.3.7. Convergence for Discounted Problems p. 222
5.4. Optimistic Policy Iteration p. 224
5.5. Simulation Based Value Iteration p. 237
Contents vii
5.6. Q Learning p. 245
5.7. Notes and Sources p. 251
6. Approximate DP with Cost to Go Function
Approximation p. 255
6.1. Generic Issues From Parameters to Policies p. 259
6.1.1. Generic Error Bounds p. 262
6.1.2. Multistage Lookahead Variations p. 264
6.1.3. Rollout Policies p. 266
6.1.4. Trading off Control Space Complexity with
State Space Complexity p. 268
6.2. Approximate Policy Iteration p. 269
6.2.1. Approximate Policy Iteration Based on
Monte Carlo Simulation p. 270
6.2.2. Error Bounds for Approximate Policy Iteration ... p. 275
6.2.3. Tightness of the Error Bounds and Empirical Behavior p. 282
6.3. Approximate Policy Evaluation Using TD(A) p. 284
6.3.1. Approximate Policy Evaluation Using TD(1) .... p. 285
6.3.2. TD(A) for General A p. 287
6.3.3. TD(A) with Linear Architectures Discounted
Problems p. 294
6.3.4. TD(A) with Linear Architectures Stochastic Shortest
Path Problems p. 308
6.4. Optimistic Policy Iteration p. 312
6.4.1. Analysis of Optimistic Policy Iteration p. 318
6.4.2. Oscillation of Policies in Optimistic Policy Iteration . p. 320
6.5. Approximate Value Iteration p. 329
6.5.1. Sequential Backward Approximation for
Finite Horizon Problems p. 329
6.5.2. Sequential Approximation in State Space p. 331
6.5.3. Sequential Backward Approximation for
Infinite Horizon Problems p. 331
6.5.4. Incremental Value Iteration p. 335
6.6. Q Learning and Advantage Updating p. 337
6.6.1. (Q Learning and Policy Iteration p. 338
6.6.2. Advantage Updating p. 339
6.7. Value Iteration with State Aggregation p. 341
6.7.1. A Method Based on Value Iteration p. 342
6.7.2. Relation to an Auxiliary Problem p. 343
6.7.3. Convergence Results p. 344
6.7.4. Error Bounds p. 349
6.7.5. Comparison with TD(0) p. 351
6.7.6. Discussion of Sampling Mechanisms p. 352
viii Contents
6.7.7. The Model Free Case p. 352
6.8. Euclidean Contractions and Optimal Stopping p. 353
6.8.1. Assumptions and Main Convergence Result p. 353
6.8.2. Error Bounds p. 357
6.8.3. Applicability of the Result p. 358
6.8.4. Q Learning for Optimal Stopping Problems p. 358
6.9. Value Iteration with Representative States p. 362
6.10. Bellman Error Methods p. 364
6.10.1. The Case of a Single Policy p. 366
6.10.2. Approximation of the Q Factors p. 367
6.10.3. Another Variant p. 368
6.10.4. Discussion and Related Methods p. 369
6.11. Continuous States and the Slope of the Cost to Go .... p. 370
6.12. Approximate Linear Programming p. 375
6.13. Overview p. 377
6.14. Notes and Sources p. 379
7. Extensions p. 385
7.1. Average Cost per Stage Problems p. 386
7.1.1. The Associated Stochastic Shortest Path Problem . . p. 387
7.1.2. Value Iteration Methods p. 391
7.1.3. Policy Iteration p. 397
7.1.4. Linear Programming p. 398
7.1.5. Simulation Based Value Iteration and Q Learning . . p. 399
7.1.6. Simulation Based Policy Iteration p. 405
7.1.7. Minimization of the Bellman Equation Error .... p. 408
7.2. Dynamic Games p. 408
7.2.1. Discounted Games p. 410
7.2.2. Stochastic Shortest Path Games p. 412
7.2.3. Sequential Games, Policy Iteration, and Q Learning . p. 412
7.2.4. Function Approximation Methods p. 416
7.3. Parallel Computation Issues p. 418
7.4. Notes and Sources p. 419
8. Case Studies p. 421
8.1. Parking p. 422
8.2. Football p. 426
8.3. Tctris p. 435
8.4. Combinatorial Optimization Maintenance and Repair . . p. 440
8.5. Dynamic Channel Allocation p. 448
8.6. Backgammon p. 452
8.7. Notes and Sources p. 456
Contents ix
Appendix A: Mathematical Review p. 457
A.I. Sets p. 458
A.2. Euclidean Space p. 459
A.3. Matrices p. 460
A.4. Analysis p. 462
A.5. Convex Sets and Functions p. 465
Appendix B: On Probability Theory and Markov Chains . p. 467
B.I. Probability Spaces p. 468
B.2. Random Variables p. 469
B.3. Conditional Probability p. 470
B.4. Stationary Markov Chains p. 471
B.5. Classification of States p. 472
B.6. Limiting Probabilities p. 472
B.7. First Passage Times p. 473
References p. 475
Index p. 487
|
| any_adam_object | 1 |
| author | Bertsekas, Dimitri P. 1942- Tsitsiklis, John N. 1958- |
| author_GND | (DE-588)171165519 (DE-588)170583996 |
| author_facet | Bertsekas, Dimitri P. 1942- Tsitsiklis, John N. 1958- |
| author_role | aut aut |
| author_sort | Bertsekas, Dimitri P. 1942- |
| author_variant | d p b dp dpb j n t jn jnt |
| building | Verbundindex |
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| callnumber-subject | QA - Mathematics |
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| dewey-full | 006.32 519.7/03 |
| dewey-hundreds | 000 - Computer science, information, general works 500 - Natural sciences and mathematics |
| dewey-ones | 006 - Special computer methods 519 - Probabilities and applied mathematics |
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| dewey-search | 006.32 519.7/03 |
| dewey-sort | 16.32 |
| dewey-tens | 000 - Computer science, information, general works 510 - Mathematics |
| discipline | Informatik Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV015264189 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T11:10:08Z |
| institution | BVB |
| isbn | 1886529108 |
| language | English |
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| open_access_boolean | |
| owner | DE-20 DE-703 DE-91G DE-BY-TUM DE-91 DE-BY-TUM DE-384 DE-634 DE-83 DE-11 DE-355 DE-BY-UBR DE-706 DE-739 DE-898 DE-BY-UBR |
| owner_facet | DE-20 DE-703 DE-91G DE-BY-TUM DE-91 DE-BY-TUM DE-384 DE-634 DE-83 DE-11 DE-355 DE-BY-UBR DE-706 DE-739 DE-898 DE-BY-UBR |
| physical | XIII, 491 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Athena Scientific |
| record_format | marc |
| series | Athena Scientific optimization and computation series |
| series2 | Athena Scientific optimization and computation series |
| spellingShingle | Bertsekas, Dimitri P. 1942- Tsitsiklis, John N. 1958- Neuro-dynamic programming Athena Scientific optimization and computation series Approximation stochastique ram Programmation dynamique ram Réseaux neuronaux (informatique) ram Apprentissage par renforcement (Intelligence artificielle) Approximation stochastique Dynamische programmering gtt Inteligencia artificial larpcal Intelligence artificielle ram Neurale netwerken gtt Optimaliseren gtt Optimisation mathématique ram Programacao dinamica larpcal Programmation dynamique Réseaux neuronaux (Informatique) optimisation mathématique inriac programmation dynamique inriac réseau neuronal inriac Künstliche Intelligenz Dynamic programming Mathematical optimization Neural networks (Computer science) Neuronales Netz (DE-588)4226127-2 gnd Dynamische Optimierung (DE-588)4125677-3 gnd |
| subject_GND | (DE-588)4226127-2 (DE-588)4125677-3 |
| title | Neuro-dynamic programming |
| title_auth | Neuro-dynamic programming |
| title_exact_search | Neuro-dynamic programming |
| title_full | Neuro-dynamic programming Dimitri P. Bertsekas and John N. Tsitsiklis |
| title_fullStr | Neuro-dynamic programming Dimitri P. Bertsekas and John N. Tsitsiklis |
| title_full_unstemmed | Neuro-dynamic programming Dimitri P. Bertsekas and John N. Tsitsiklis |
| title_short | Neuro-dynamic programming |
| title_sort | neuro dynamic programming |
| topic | Approximation stochastique ram Programmation dynamique ram Réseaux neuronaux (informatique) ram Apprentissage par renforcement (Intelligence artificielle) Approximation stochastique Dynamische programmering gtt Inteligencia artificial larpcal Intelligence artificielle ram Neurale netwerken gtt Optimaliseren gtt Optimisation mathématique ram Programacao dinamica larpcal Programmation dynamique Réseaux neuronaux (Informatique) optimisation mathématique inriac programmation dynamique inriac réseau neuronal inriac Künstliche Intelligenz Dynamic programming Mathematical optimization Neural networks (Computer science) Neuronales Netz (DE-588)4226127-2 gnd Dynamische Optimierung (DE-588)4125677-3 gnd |
| topic_facet | Approximation stochastique Programmation dynamique Réseaux neuronaux (informatique) Apprentissage par renforcement (Intelligence artificielle) Dynamische programmering Inteligencia artificial Intelligence artificielle Neurale netwerken Optimaliseren Optimisation mathématique Programacao dinamica Réseaux neuronaux (Informatique) optimisation mathématique programmation dynamique réseau neuronal Künstliche Intelligenz Dynamic programming Mathematical optimization Neural networks (Computer science) Neuronales Netz Dynamische Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010098849&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV015264203 |
| work_keys_str_mv | AT bertsekasdimitrip neurodynamicprogramming AT tsitsiklisjohnn neurodynamicprogramming |
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