Constrained Markov Decision Processes

Eitan Altman, Shaler Stidham Jr. (University of North Carolina, Chapel Hill, USA), Marco Scarsini (University of Torino, Torino, Italy) , Moshe Shaked (University of Arizona, Tucson, Arizona, USA)

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English

Chapman & Hall/CRC
30 March 1999

Probability & statistics; Stochastics

Series: Stochastic Modeling Series

This book provides a unified approach for the study of constrained Markov decision processes with a finite state space and unbounded costs. Unlike the single controller case considered in many other books, the author considers a single controller with several objectives, such as minimizing delays and loss, probabilities, and maximization of throughputs. It is desirable to design a controller that minimizes one cost objective, subject to inequality constraints on other cost objectives. This framework describes dynamic decision problems arising frequently in many engineering fields.

A thorough overview of these applications is presented in the introduction. The book is then divided into three sections that build upon each other.

The first part explains the theory for the finite state space. The author characterizes the

set of achievable expected occupation measures as well as performance vectors, and identifies simple classes of policies among which optimal policies exist. This allows the reduction of the original dynamic into a linear program. A Lagranian approach is then used to derive the

dual linear program using dynamic programming techniques.

In

the second part, these results are extended to the infinite

state space and action spaces. The author provides two frameworks: the case where costs are bounded below and the contracting framework. The third part builds upon the results of the first two parts and examines asymptotical results of the

convergence of both the value and the policies in the time horizon and in the discount factor. Finally, several state truncation algorithms that enable the approximation of the solution of the original control problem via finite linear programs are given.

By: Eitan Altman
Series edited by: Shaler Stidham Jr. (University of North Carolina Chapel Hill USA), Marco Scarsini (University of Torino, Torino, Italy), Moshe Shaked (University of Arizona, Tucson, Arizona, USA)
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Volume: 7
Dimensions: Height: 229mm, Width: 152mm, Spine: 19mm
Weight: 498g
ISBN: 9780849303821
ISBN 10: 0849303826
Series: Stochastic Modeling Series
Pages: 256
Publication Date: 30 March 1999
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Altman, Eitan