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EXISTENCE OF OPTIMAL STATIONARY POLICIES IN FINITE DYNAMIC PROGRAMS WITH NONNEGATIVE REWARDS

AN ALTERNATIVE APPROACH

Published online by Cambridge University Press:  11 January 2002

Rolando Cavazos-Cadena
Affiliation:
Departamento de Estadística y Cálculo, Universidad Autónoma Agraria Antonio Narro, Buenavista, Saltillo, México, E-mail: rcavazos@narro.uaaan.mx Centro de Investigaciones Socioeconómicas, Universidad Autónoma de Coahuila, Unidad Campo Redondo, Saltillo, México, E-mail: rcavcad@cise.uadec.mx
Raúl Montes-de-Oca
Affiliation:
Departamento de Matemáticas, Universidad Autónoma Metropolitana, Vicentina, México, México, E-mail: momr@xanum.uam.mx
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Abstract

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This article concerns Markov decision chains with finite state and action spaces, and a control policy is graded via the expected total-reward criterion associated to a nonnegative reward function. Within this framework, a classical theorem guarantees the existence of an optimal stationary policy whenever the optimal value function is finite, a result that is obtained via a limit process using the discounted criterion. The objective of this article is to present an alternative approach, based entirely on the properties of the expected total-reward index, to establish such an existence result.

Type
Research Article
Copyright
© 2001 Cambridge University Press