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Nonstationary value iteration in controlled Markov chains with risk-sensitive average criterion

Part of: Stochastic systems and control

Published online by Cambridge University Press:  14 July 2016

Rolando Cavazos-Cadena  and
Raúl Montes-De-Oca
Rolando Cavazos-Cadena*
Affiliation:
Universidad Autónoma Agraria Antonio Narro
Raúl Montes-De-Oca*
Affiliation:
Universidad Autónoma Metropolitana
*
∗Postal address: Departamento de Estadística y Cálculo, Universidad Autónoma Agraria Antonio Narro, Buenavista, Saltillo COAH, 25315, México. Email address: rcavazos@narro.uaaan.mx
∗∗Postal address: Departamento de Matemáticas, Universidad Autónoma Metropolitana, Campus Iztapalapa, Avenida San Rafael Atlixco #186, Colonia Vicentina, México 09340, D.F. México. Email address: momr@xanum.uam.mx
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Abstract

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This work concerns Markov decision chains with finite state spaces and compact action sets. The performance index is the long-run risk-sensitive average cost criterion, and it is assumed that, under each stationary policy, the state space is a communicating class and that the cost function and the transition law depend continuously on the action. These latter data are not directly available to the decision-maker, but convergent approximations are known or are more easily computed. In this context, the nonstationary value iteration algorithm is used to approximate the solution of the optimality equation, and to obtain a nearly optimal stationary policy.

Keywords

Nonstationary successive approximations algorithmapproximate solution to the optimality equationSchweitzer's transformationBirkhoff's contraction coefficient

MSC classification

Primary: 90C40: Markov and semi-Markov decision processes 93E20: Optimal stochastic control
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 4 , December 2005 , pp. 905 - 918
Copyright
© Applied Probability Trust 2005 

Footnotes

This work was supported by the PSF Organization under grant no. 008/100/03-3.

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