Prediction, learning, and games:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2006
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XII, 394 S. Diagramme |
| ISBN: | 0521841089 9780521841085 |
Internformat
MARC
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| 245 | 1 | 0 | |a Prediction, learning, and games |c Nicolò Cesa-Bianchi ; Gábor Lugosi |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2006 | |
| 300 | |a XII, 394 S. |b Diagramme | ||
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Datensatz im Suchindex
| _version_ | 1804140633430949888 |
|---|---|
| adam_text | Contents
Preface page xi
1 Introduction 1
1.1 Prediction 1
1.2 Learning 3
1.3 Games 3
1.4 A Gentle Start 4
1.5 A Note to the Reader 6
2 Prediction with Expert Advice 7
2.1 Weighted Average Prediction 9
2.2 An Optimal Bound 15
2.3 Bounds That Hold Uniformly over Time 17
2.4 An Improvement for Small Losses 20
2.5 Forecasters Using the Gradient of the Loss 22
2.6 Scaled Losses and Signed Games 24
2.7 The Multilinear Forecaster 25
2.8 The Exponential Forecaster for Signed
Games 27
2.9 Simulatable Experts 29
2.10 Minimax Regret 30
2.11 Discounted Regret 32
2.12 Bibliographic Remarks 34
2.13 Exercises 37
3 Tight Bounds for Specific Losses 40
3.1 Introduction 40
3.2 Follow the Best Expert 41
3.3 Exp-concave Loss Functions 45
3.4 The Greedy Forecaster 49
3.5 The Aggregating Forecaster 52
3.6 Mixability for Certain Losses 56
3.7 General Lower Bounds 59
3.8 Bibliographic Remarks 63
3.9 Exercises 64
vii
viii Contents
4 Randomized Prediction 67
4.1 Introduction 67
4.2 Weighted Average Forecasters 71
4.3 Follow the Perturbed Leader 74
4.4 Internal Regret 79
4.5 Calibration 85
4.6 Generalized Regret 90
4.7 Calibration with Checking Rules 93
4.8 Bibliographic Remarks 94
4.9 Exercises 95
5 Efficient Forecasters for Large Classes of Experts 99
5.1 Introduction 99
5.2 Tracking the Best Expert 100
5.3 Tree Experts 109
5.4 The Shortest Path Problem 116
5.5 Tracking the Best of Many Actions 121
5.6 Bibliographic Remarks 124
5.7 Exercises 125
6 Prediction with Limited Feedback 128
6.1 Introduction 128
6.2 Label Efficient Prediction 129
6.3 Lower Bounds 136
6.4 Partial Monitoring 143
6.5 A General Forecaster for Partial Monitoring 146
6.6 Hannan Consistency and Partial Monitoring 153
6.7 Multi-armed Bandit Problems 156
6.8 An Improved Bandit Strategy 160
6.9 Lower Bounds for the Bandit Problem 164
6.10 How to Select the Best Action 169
6.11 Bibliographic Remarks 173
6.12 Exercises 175
7 Prediction and Playing Games 180
7.1 Games and Equilibria 180
7.2 Minimax Theorems 185
7.3 Repeated Two-Player Zero-Sum Games 187
7.4 Correlated Equilibrium and Internal Regret 190
7.5 Unknown Games: Game-Theoretic Bandits 194
7.6 Calibration and Correlated Equilibrium 194
7.7 Blackwell s Approachability Theorem 197
7.8 Potential-based Approachability 202
7.9 Convergence to Nash Equilibria 205
7.10 Convergence in Unknown Games 210
7.11 Playing Against Opponents That React 219
7.12 Bibliographic Remarks 225
7.13 Exercises 227
Contents ix
8 Absolute Loss 233
8.1 Simulatable Experts 233
8.2 Optimal Algorithm for Simulatable Experts 234
8.3 Static Experts 236
8.4 A Simple Example 238
8.5 Bounds for Classes of Static Experts 239
8.6 Bounds for General Classes 241
8.7 Bibliographic Remarks 244
8.8 Exercises 245
9 Logarithmic Loss 247
9.1 Sequential Probability Assignment 247
9.2 Mixture Forecasters 249
9.3 Gambling and Data Compression 250
9.4 The Minimax Optimal Forecaster 252
9.5 Examples 253
9.6 The Laplace Mixture 256
9.7 A Refined Mixture Forecaster 258
9.8 Lower Bounds for Most Sequences 261
9.9 Prediction with Side Information 263
9.10 A General Upper Bound 265
9.11 Further Examples 269
9.12 Bibliographic Remarks 271
9.13 Exercises 272
10 Sequential Investment 276
10.1 Portfolio Selection 276
10.2 The Minimax Wealth Ratio 278
10.3 Prediction and Investment 278
10.4 Universal Portfolios 282
10.5 The EG Investment Strategy 284
10.6 Investment with Side Information 287
10.7 Bibliographic Remarks 289
10.8 Exercises 290
11 Linear Pattern Recognition 293
11.1 Prediction with Side Information 293
11.2 Bregman Divergences 294
11.3 Potential-Based Gradient Descent 298
11.4 The Transfer Function 301
11.5 Forecasters Using Bregman Projections 307
11.6 Time-Varying Potentials 314
11.7 The Elliptic Potential 316
11.8 A Nonlinear Forecaster 320
11.9 Lower Bounds 322
11.10 Mixture Forecasters 325
11.11 Bibliographic Remarks 328
11.12 Exercises 330
x Contents
12 Linear Classification 333
12.1 The Zero-One Loss 333
12.2 The Hinge Loss 335
12.3 Maximum Margin Classifiers 343
12.4 Label Efficient Classifiers 346
12.5 Kernel-Based Classifiers 350
12.6 Bibliographic Remarks 355
12.7 Exercises 356
Appendix 359
A.I Inequalities from Probability Theory 359
A.1.1 Hoeffding s Inequality 359
A.I.2 Bernstein s Inequality 361
A. 1.3 Hoeffding-Azuma Inequality and Related Results 362
A. 1.4 Khinchine s Inequality 364
A. 1.5 Slud s Inequality 364
A. 1.6 A Simple Limit Theorem 364
A. 1.7 Proof of Theorem 8.3 367
A. 1.8 Rademacher Averages 368
A. 1.9 The Beta Distribution 369
A.2 Basic Information Theory 370
A.3 Basics of Classification 371
References 373
Author Index 387
Subject Index 390
|
| any_adam_object | 1 |
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| discipline | Informatik Mathematik Wirtschaftswissenschaften |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV024615182 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:03:05Z |
| institution | BVB |
| isbn | 0521841089 9780521841085 |
| language | English |
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| spelling | Cesa-Bianchi, Nicolò 1963- Verfasser (DE-588)120314797 aut Prediction, learning, and games Nicolò Cesa-Bianchi ; Gábor Lugosi 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2006 XII, 394 S. Diagramme txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Spieltheorie (DE-588)4056243-8 gnd rswk-swf Maschinelles Lernen (DE-588)4193754-5 gnd rswk-swf Vorhersagetheorie (DE-588)4188671-9 gnd rswk-swf Spieltheorie (DE-588)4056243-8 s Vorhersagetheorie (DE-588)4188671-9 s Maschinelles Lernen (DE-588)4193754-5 s DE-604 Lugosi, Gábor 1964- Verfasser (DE-588)17173677X aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018587580&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cesa-Bianchi, Nicolò 1963- Lugosi, Gábor 1964- Prediction, learning, and games Spieltheorie (DE-588)4056243-8 gnd Maschinelles Lernen (DE-588)4193754-5 gnd Vorhersagetheorie (DE-588)4188671-9 gnd |
| subject_GND | (DE-588)4056243-8 (DE-588)4193754-5 (DE-588)4188671-9 |
| title | Prediction, learning, and games |
| title_auth | Prediction, learning, and games |
| title_exact_search | Prediction, learning, and games |
| title_full | Prediction, learning, and games Nicolò Cesa-Bianchi ; Gábor Lugosi |
| title_fullStr | Prediction, learning, and games Nicolò Cesa-Bianchi ; Gábor Lugosi |
| title_full_unstemmed | Prediction, learning, and games Nicolò Cesa-Bianchi ; Gábor Lugosi |
| title_short | Prediction, learning, and games |
| title_sort | prediction learning and games |
| topic | Spieltheorie (DE-588)4056243-8 gnd Maschinelles Lernen (DE-588)4193754-5 gnd Vorhersagetheorie (DE-588)4188671-9 gnd |
| topic_facet | Spieltheorie Maschinelles Lernen Vorhersagetheorie |
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