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This important new text and reference for researchers and students in machine learning, game theory, statistics and information theory offers the first comprehensive treatment of the problem of predicting individual sequences. Unlike standard statistical approaches to forecasting, prediction of individual sequences does not impose any probabilistic assumption on the data-generating mechanism. Yet, prediction algorithms can be c***tructed that work well for all possible sequences, in the sense that their performance is always nearly as good as the best forecasting strategy in a given reference class. The central theme is the model of prediction using expert advice, a general framework within which many related problems can be cast and discussed. Repeated game playing, adaptive data compression, sequential investment in the stock market, sequential pattern ***ysis, and several other problems are viewed as instances of the experts' framework and ***yzed from a common n***tochastic standpoint that often reveals new and intriguing connecti***. Old and new forecasting methods are described in a mathematically precise way in order to characterize their theoretical limitati*** and possibilities.

Preface

1 Introduction

　1.1 Prediction

　1.2 Learning

　1.3 Games

　1.4 A Gentle Start

　1.5 A Note to the Reader

2 Prediction with Expert Advice

　2.1 Weighted Average Prediction

　2.2 An Optimal Bound

　2.3 Bounds That Hold Uniformly over Time

　2.4 An Improvement for Small Losses

　2.5 Forecasters Using the Gradient of the Loss

　2.6 Scaled Losses and Signed Games

　2.7 The Multilinear Forecaster

　2.8 The Exponential Forecaster for Signed Games

　2.9 Simulatable Experts

　2.10 Minimax Regret

　2.11 Discounted Regret

　2.12 Bibliographic Remarks

　2.13 Exercises

3 Tight Bounds for Specific Losses

　3.1 Introduction

　3.2 Follow the Best Expert

　3.3 Exp-concave Loss Functi***

　3.4 The Greedy Forecaster

　3.5 The Aggregating Forecaster

　3.6 Mixability for Certain Losses

　3.7 General Lower Bounds

　3.8 Bibliographic Remarks

　3.9 Exercises

4 Randomized Prediction

　4.1 Introduction

　4.2 Weighted Average Forecasters

　4.3 Follow the Perturbed Leader

　4.4 Internal Regret

　4.5 Calibration

　4.6 Generalized Regret

　4.7 Calibration with Checking Rules

　4.8 Bibliographic Remarks

　4.9 Exercises

5 Efficient Forecasters for Large Classes of Experts

　5.1 Introduction

　5.2 Tracking the Best Expert

　5.3 Tree Experts

　5.4 The Shortest Path Problem

　5.5 Tracking the Best of Many Acti***

　5.6 Bibliographic Remarks

　5.7 Exercises

6 Prediction with Limited Feedback

　6.1 Introduction

　6.2 Label Efficient Prediction

　6.3 Lower Bounds

　*** Partial Monitoring

　6.5 A General Forecaster for Partial Monitoring

　6.6 Hannah C***istency and Partial Monitoring

　6.7 Multi-armed Bandit Problems

　6.8 An Improved Bandit Strategy

　6.9 Lower Bounds for the Bandit Problem

　6.10 How to Select the Best Action

　6.11 Bibliographic Remarks

　6.12 Exercises

7 Prediction and Playing Games

　7.1 Games and Equilibria

　7.2 Minimax Theorems

　7.3 Repeated Two-Player Zero-Sum Games

　7.4 Correlated Equilibrium and Internal Regret

　7.5 Unknown Games: Game-Theoretic Bandits

　7.6 Calibration and Correlated Equilibrium

　7.7 Blackwell's Approachability Theorem

　7.8 Potential-based Approachability

　7.9 Convergence to Nash Equilibria

　7.10 Convergence in Unknown Games

　7.11 Playing Against Opponents That React

　7.12 Bibliographic Remarks

　7.13 Exercises

8　Absolute loss

9　Logarithmic loss

10　Sequential investment

11　Linear pattern recognition

12　Linear classification

Appendix

References

Author Index

Subject Index

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作者简介：

　　Nicolò Cesa-Bianchi is Professor of Computer Science at the University of Milan, Italy. His research interests include learning theory, pattern ***ysis, and worst-case ***ysis of algorithms. He is action editor of The Machine Learning Journal. Gábor Lugosi has been working on various problems in pattern classification, nonparametric statistics, statistical learning theory, game theory, probability, and information theory. He is co-author of the monographs, A Probabilistic Theory of Pattern Recognition and Combinatorial Methods of Density Estimation. He has been an associate editor of various journals including The IEEE Transacti*** of Information Theory, Test, ESAIM: Probability and Statistics and Statistics and Decisi***.