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The optimality equation in average cost denumerable state semi-Markov decision problems, recurrency conditions and algorithms

Published online by Cambridge University Press:  14 July 2016

A. Federgruen  and
H. C. Tijms
A. Federgruen
Affiliation:
Mathematisch Centrum, Amsterdam
H. C. Tijms
Affiliation:
Vrije Universiteit, Amsterdam
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Abstract

This paper is concerned with the optimality equation for the average costs in a denumerable state semi-Markov decision model. It will be shown that under each of a number of recurrency conditions on the transition probability matrices associated with the stationary policies, the optimality equation has a bounded solution. This solution indeed yields a stationary policy which is optimal for a strong version of the average cost optimality criterion. Besides the existence of a bounded solution to the optimality equation, we will show that both the value-iteration method and the policy-iteration method can be used to determine such a solution. For the latter method we will prove that the average costs and the relative cost functions of the policies generated converge to a solution of the optimality equation.

Keywords

SEMI-MARKOV DECISION MODELDENUMERABLE STATE SPACEAVERAGE COSTSOPTIMALITY EQUATIONRECURRENCY CONDITIONSVALUE-ITERATION METHODPOLICY-ITERATION METHODCONVERGENCE RESULTS
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 2 , June 1978 , pp. 356 - 373
Copyright
Copyright © Applied Probability Trust 1978 

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