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Average sample-path optimality for continuous-time Markov decision processes in Polish spaces

Average sample-path optimality for continuous-time Markov decision processes in Polish spaces In this paper we study the average sample-path cost (ASPC) problem for continuous-time Markov decision processes in Polish spaces. To the best of our knowledge, this paper is a first attempt to study the ASPC criterion on continuous-time MDPs with Polish state and action spaces. The corresponding transition rates are allowed to be unbounded, and the cost rates may have neither upper nor lower bounds. Under some mild hypotheses, we prove the existence of ɛ (ɛ ≥ 0)-ASPC optimal stationary policies based on two different approaches:one is the “optimality equation” approach and the other is the “two optimality inequalities” approach. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Average sample-path optimality for continuous-time Markov decision processes in Polish spaces

Acta Mathematicae Applicatae Sinica , Volume 27 (4) – Sep 9, 2011

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References (28)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Theoretical, Mathematical and Computational Physics; Math Applications in Computer Science
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-011-0111-9
Publisher site
See Article on Publisher Site

Abstract

In this paper we study the average sample-path cost (ASPC) problem for continuous-time Markov decision processes in Polish spaces. To the best of our knowledge, this paper is a first attempt to study the ASPC criterion on continuous-time MDPs with Polish state and action spaces. The corresponding transition rates are allowed to be unbounded, and the cost rates may have neither upper nor lower bounds. Under some mild hypotheses, we prove the existence of ɛ (ɛ ≥ 0)-ASPC optimal stationary policies based on two different approaches:one is the “optimality equation” approach and the other is the “two optimality inequalities” approach.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Sep 9, 2011

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