Finite Approximations in Discrete-Time Stochastic Control

Quantized Models and Asymptotic Optimality

Naci Saldi, Tamás Linder, Serdar Yüksel (Autoren)

Buch | Hardcover

VII, 198 Seiten

2018 | 1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-79032-9 (ISBN)

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In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for discretization of actions, and the computational approach for discretization of states and actions. Part I of the text discusses Markov decision processes and their finite-state or finite-action approximations, while Part II builds from there to finite approximations in decentralized stochastic control problems.
This volume is perfect for researchers and graduate students interested in stochastic controls. With the tools presented, readers will be able to establish the convergence of approximation models to original models and the methods are general enough that researchers can build corresponding approximation results, typically with no additional assumptions.

Introduction and Summary.- Part I: Finite Model Approximations in Stochastic Control.- Prelude to Part I.- Finite Action Approximation of Markov Decision Processes.- Finite-State Approximation of Markov Decision Processes.- Approximations for Partially Observed Markov Decision Processes.- Approximations for Constrained Markov Decision Problems.- Part II: Finite Model Approximations in Decentralized Stochastic Control.- Prelude to Part II.- Finite Model Approximations in Decentralized Stochastic Control.- Asymptotic Optimality of Finite Models for Specific Systems.- Index.- References.

"The book is very well written, with focus on clarity ... . material of this monograph is pretty advanced, the presentation style is very clear, compact and relatively easy to follow, but at the same time mathematically rigorous. The monograph is a good piece of work on a subject that attracts considerable attention. Both researchers and professionals in applied mathematics will find this book very useful. It can also be recommended as a valuable reference text in approximate dynamic programming." (Dariusz Ucinski, zbMATH 1471.93005, 2021)

"This book is an interesting and complete treatise on finite approximations of different kinds of discrete-time stochastic control problems. It is based on several recent research results on the topic presented which have been published in various papers written by the authors." (Raúl Montes-de-Oca, Mathematical Reviews, March, 2019)

Erscheinungsdatum	08.06.2018
Reihe/Serie	Systems & Control: Foundations & Applications
Zusatzinfo	VII, 198 p. 6 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	479 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	asymptotic optimality • decentralized stochastic control • finite state approximations • Markov Decision Processes • numerical approximation • Quantization • stochastic control
ISBN-10	3-319-79032-3 / 3319790323
ISBN-13	978-3-319-79032-9 / 9783319790329
Zustand	Neuware