Finite approximations in discrete-time stochastic control. Quantized models and asymptotic optimality
type: Item
instance of: scholarly article
title: Finite approximations in discrete-time stochastic control. Quantized models and asymptotic optimality
zbMATH Open document ID: 1471.93005
DOI: 10.1007/978-3-319-79033-6
author: Naci Saldi
author: Tamás Linder
author: Serdar Yüksel
published in: Systems \& Control: Foundations \& Applications
publication date: 2018-04-23T00:00:00Z
review text: The monograph constitutes an extremely valuable addition to the literature on approximate dynamic programming. It is aimed at expounding in a unified framework numerous original results that the three authors have achieved in the area of approximation of centralized and decentralized discrete-time stochastic control problems with uncountable state, measurement, and action spaces using quantization methods. The work reported therein, originally scattered over journal and conference papers, is extremely extensive and ranges from different optimality criteria (discounted cost and average cost problems) to cost-constrained models to partially observed processes to decentralized stochastic control problems. The authors adopt quite an abstract setting based on Borel state and action spaces, but this does not mean that the monograph can be of interest only for researchers concerned with advanced stochastic control theory. This generality is an invaluable asset, as the framework can be employed to many nonstandard settings encountered in theory and applications. The authors exploit it themselves to develop approximation methods for partially observed Markov decision processes. The book is very well written, with focus on clarity, which is a result of the authors' great mathematical erudition. On the one hand, there are no algorithms included (only some simple numerical examples complement the presented theoretical results), but these can be found in on other contributions. On the other hand, however, the book provides rigorous and flexible theoretical basis for the presented discretization methods and the attendant convergence characterizations. The authors show that quantization, which reduces a system with Borel spaces to one with finite state, measurement, and action spaces, constitutes an extremely constructive method which essentially does not depend on the system under consideration. What is more, they derive bounds on the approximation performance. Compared with the …
reviewed by: Dariusz Uciński
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 93A14
Mathematics Subject Classification ID: 90C40
Mathematics Subject Classification ID: 60J20
zbMATH DE Number: 6863966
zbMATH Keywords: discrete-time stochastic control
zbMATH Keywords: asymptotic optimality
zbMATH Keywords: decentralized stochastic control
zbMATH Keywords: Markov decision process
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-79033-6
OpenAlex ID: W4253349640
description: scientific article; zbMATH DE number 6863966