Finite Approximations in Discrete-Time Stochastic Control

Quantized Models and Asymptotic Optimality
 
 
Birkhäuser (Verlag)
  • erschienen am 16. Juni 2018
 
  • Buch
  • |
  • Hardcover
  • |
  • VII, 198 Seiten
978-3-319-79032-9 (ISBN)
 
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.
Book
1st ed. 2018
  • Englisch
  • Cham
  • |
  • Schweiz
Springer International Publishing
  • Für Beruf und Forschung
  • 6 s/w Abbildungen
  • |
  • 6 schwarz-weiße Abbildungen, Bibliographie
  • Höhe: 241 mm
  • |
  • Breite: 159 mm
  • |
  • Dicke: 20 mm
  • 465 gr
978-3-319-79032-9 (9783319790329)
3-319-79032-3 (3319790323)
10.1007/978-3-319-79033-6
weitere Ausgaben werden ermittelt
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.
"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." (Raul Montes-de-Oca, Mathematical Reviews, March, 2019)
 
"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." (Raul Montes-de-Oca, Mathematical Reviews, March, 2019)

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