John Gittins, Kevin Glazebrook, Richard Weber

Multi-armed Bandit Allocation Indices (eBook, PDF)

• Format: PDF

Produktbeschreibung

In 1989 the first edition of this book set out Gittins' pioneering index solution to the multi-armed bandit problem and his subsequent investigation of a wide of sequential resource allocation and stochastic scheduling problems. Since then there has been a remarkable flowering of new insights, generalizations and applications, to which Glazebrook and Weber have made major contributions. This second edition brings the story up to date. There are new chapters on the achievable region approach to stochastic optimization problems, the construction of performance bounds for suboptimal policies, Whittle's restless bandits, and the use of Lagrangian relaxation in the construction and evaluation of index policies. Some of the many varied proofs of the index theorem are discussed along with the insights that they provide. Many contemporary applications are surveyed, and over 150 new references are included. Over the past 40 years the Gittins index has helped theoreticians and practitioners to address a huge variety of problems within chemometrics, economics, engineering, numerical analysis, operational research, probability, statistics and website design. This new edition will be an important resource for others wishing to use this approach.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 312
• Erscheinungstermin: 1. Januar 2011
• Englisch
• ISBN-13: 9780470980040
• Artikelnr.: 37301411

Autorenporträt

John Gittins, Statistics Department, University of Oxford, UK Kevin Glazebrook, Department of Management Science, Lancaster University, UK Richard Weber, Statistical Laboratory, University of Cambridge, UK

Inhaltsangabe

Foreword. Foreword to the first edition. Preface. Preface to the first
edition. 1 Introduction or Exploration. Exercises. 2 Main Ideas: Gittins
Index. 2.1 Introduction. 2.2 Decision processes. 2.3 Simple families of
alternative bandit processes. 2.4 Dynamic programming. 2.5 Gittins index
theorem. 2.6 Gittins index. 2.7 Proof of the index theorem by interchanging
bandit portions. 2.8 Continuous-time bandit processes. 2.9 Proof of the
index theorem by induction and interchange argument. 2.10 Calculation of
Gittins indices. 2.11 Monotonicity conditions. 2.12 History of the index
theorem. 2.13 Some decision process theory. Exercises. 3 Necessary
Assumptions for Indices. 3.1 Introduction. 3.2 Jobs. 3.3 Continuous-time
jobs. 3.4 Necessary assumptions. 3.5 Beyond the necessary assumptions.
Exercises. 4 Superprocesses, Precedence Constraints and Arrivals. 4.1
Introduction. 4.2 Bandit superprocesses. 4.3 The index theorem for
superprocesses. 4.4 Stoppable bandit processes. 4.5 Proof of the index
theorem by freezing and promotion rules. 4.6 The index theorem for jobs
with precedence constraints. 4.7 Precedence constraints forming an
out-forest. 4.8 Bandit processes with arrivals. 4.9 Tax problems. 4.10 Near
optimality of nearly index policies. Exercises. 5 The Achievable Region
Methodology. 5.1 Introduction. 5.2 A simple example. 5.3 Proof of the index
theorem by greedy algorithm. 5.4 Generalized conservation laws and
indexable systems. 5.5 Performance bounds for policies for branching
bandits. 5.6 Job selection and scheduling problems. 5.7 Multi-armed bandits
on parallel machines. Exercises. 6 Restless Bandits and Lagrangian
Relaxation. 6.1 Introduction. 6.2 Restless bandits. 6.3 Whittle indices for
restless bandits. 6.4 Asymptotic optimality. 6.5 Monotone policies and
simple proofs of indexability. 6.6 Applications to multi-class queuing
systems. 6.7 Performance bounds for the Whittle index policy. 6.8 Indices
for more general resource configurations. Exercises. 7 Multi-Population
Random Sampling (Theory). 7.1 Introduction. 7.2 Jobs and targets. 7.3 Use
of monotonicity properties. 7.4 General methods of calculation: use of
invariance properties. 7.5 Random sampling times. 7.6 Brownian reward
processes. 7.7 Asymptotically normal reward processes. 7.8 Diffusion
bandits. Exercises. 8 Multi-Population Random Sampling (Calculations). 8.1
Introduction. 8.2 Normal reward processes (known variance). 8.3 Normal
reward processes (mean and variance both unknown). 8.4 Bernoulli reward
processes. 8.5 Exponential reward processes. 8.6 Exponential target
process. 8.7 Bernoulli/exponential target process. Exercises. 9 Further
Exploitation. 9.1 Introduction. 9.2 Website morphing. 9.3 Economics. 9.4
Value of information. 9.5 More on job-scheduling problems. 9.6 Military
applications. References. Tables. Index.