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Value iteration in a class of average controlled Markov chains with unbounded costs: necessary and sufficient conditions for pointwise convergence

Part of: Stochastic systems and control

Published online by Cambridge University Press:  14 July 2016

Rolando Cavazos-Cadena  and
Emmanuel Fernández-Gaucherand
Rolando Cavazos-Cadena*
Affiliation:
Universidad Autónoma Agraria Antonio Narro
Emmanuel Fernández-Gaucherand*
Affiliation:
The University of Arizona
*
∗Postal address: Departamento de Estadística y Cálculo, Universidad Autónoma Agraria Antonio Narro, Buenavista, Saltillo COAH 25315, México.
∗∗Postal address: Systems and Industrial Engineering Department, The University of Arizona, Tucson AZ 85721, USA.
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Abstract

This work concerns controlled Markov chains with denumerable state space, (possibly) unbounded cost function, and an expected average cost criterion. Under a Lyapunov function condition, together with mild continuity-compactness assumptions, a simple necessary and sufficient criterion is given so that the relative value functions and differential costs produced by the value iteration scheme converge pointwise to the solution of the optimality equation; this criterion is applied to obtain convergence results when the cost function is bounded below or bounded above.

Keywords

CONTROLLED MARKOV CHAINSAVERAGE COST CRITERIONLYAPUNOV FUNCTION CONDITIONVALUE ITERATION SCHEMEPOINTWISE CONVERGENCENECESSARY AND SUFFICIENT CONDITIONS

MSC classification

Primary: 93E20: Optimal stochastic control 90C40: Markov and semi-Markov decision processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 4 , December 1996 , pp. 986 - 1002
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

∗

Research supported by a U.S.-México Collaborative Research Program funded by the National Science Foundation under Grant NSF-INT 9201430, and by the Consejo Nacional de Ciencia y Tecnología (CONACyT), México.

∗∗

The work of Cavazos-Cadena was partially supported by the PSF Organization under Grant No. 200–150/94–01, and by the MAXTOR Foundation for Applied Probability and Statistics (MAXFAPS) under Grant No. 01–01–56/01–94.

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