Prediction, Learning, and Games - A Comprehensive Treatment of Individual Sequence Forecasting

Sep 21, 2026

Uploaded by Rowan

Prediction, Learning, and Games presents a rigorous framework for predicting individual sequences without imposing probabilistic assumptions on the data-generating mechanism. It explains how prediction algorithms can perform nearly as well as the best strategy within a chosen reference class and develops a central model based on expert advice. The text unifies repeated games, adaptive data compression, sequential investment, and sequential pattern analysis using a common nonstochastic viewpoint.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages407

Reading Time17 h 6 min

AccessFree to download

Preface

Introduction

Prediction

Learning

Games

A Gentle Start

A Note to the Reader

Prediction with Expert Advice

Weighted Average Prediction

An Optimal Bound

Bounds That Hold Uniformly over Time

An Improvement for Small Losses

Forecasters Using the Gradient of the Loss

Scaled Losses and Signed Games

The Multilinear Forecaster

The Exponential Forecaster for Signed Games

Simulatable Experts

Minimax Regret

Discounted Regret

Bibliographic Remarks

Exercises

Tight Bounds for Specific Losses

Follow the Best Expert

Exp-concave Loss Functions

The Greedy Forecaster

The Aggregating Forecaster

Mixability for Certain Losses

General Lower Bounds

Bibliographic Remarks

Exercises

Prediction, Learning, and Games 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 constructed 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 analysis, and several other problems are viewed as instances of the experts’ framework and analyzed from a common nonstochastic standpoint that often reveals new and intriguing connections. Old and new forecasting methods are described in a mathematically precise way in order to characterize their theoretical limitations and possibilities. Nicol Cesa-Bianchi is Professor of Computer Science at the University of Milan, Italy. His research interests include learning theory, pattern analysis, and worst-case analysis of algorithms. He is an action editor of the journal Machine Learning. Gbor Lugosi has been working on various problems in pattern classiﬁcation, nonparametric statistics, statistical learning theory, game theory, probability, and information theory. He is coauthor 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 Transactions of Information Theory, Test, ESAIM: Probability and Statistics, and Statistics and Decisions. Prediction, Learning, and Games NICOLO` CESA-BIANCHI Universit degli Studi di Milano GA´ BOR LUGOSI Universitat Pompeu Fabra, Barcelona cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge cb2 2ru, UK Published in the United States of America by Cambridge University Press, New York [www.cambridge.org](www.cambridge.org) Information on this [title: www.cambridge.org/9780521841085](title: www.cambridge.org/9780521841085) © Nicolo Cesa-Bianchi and Gabor Lugosi This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2006 isbn-13 978-0-511-19178-7 eBook (NetLibrary) isbn-10 0-511-19178-2 eBook (NetLibrary) isbn-13 978-0-521-84108-5 hardback isbn-10 0-521-84108-9 hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. to Betta, Silvia, and Luca – NCB to Arrate, Dani, and Frida to the memory of my parents – GL 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 Re

FAQs

What makes prediction of individual sequences different from standard forecasting approaches?

It does not impose probabilistic assumptions on the data-generating mechanism, yet constructs algorithms that perform nearly as well as the best strategy in a given reference class.

What is the central framework used to organize the book’s problems?

The model of prediction using expert advice, which provides a general framework to cast and discuss multiple related problems from a nonstochastic standpoint.

Which kinds of problems are analyzed as instances of the experts’ framework?

Repeated game playing, adaptive data compression, sequential investment in the stock market, sequential pattern analysis, and other related problems.

Sep 21, 2026

Uploaded by Rowan