Geodesic
Stationary optimal policies in a class of multichain positive dynamic programs with finite state space and risk-sensitive criterion
Rolando Cavazos-Cadena1 ; Raul Montes-de-Oca2
1 Departamento de Estadistica y Calculo Universidad Autonoma Agraria Antonio Narro Buenavista, Saltillo COAH 25315, Mexico
2 Departamento de Matematicas Universidad Autonoma Metropolitana Campus Iztapalapa Avenida Michoacan y La Purisima s//n Col. Vicentina Mexico D.F. 09340, Mexico
Applicationes Mathematicae, Tome 28 (2001) no. 1, pp. 93-109 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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This work concerns Markov decision processes with finite state space and compact action sets. The decision maker is supposed to have a constant-risk sensitivity coefficient, and a control policy is graded via the risk-sensitive expected total-reward criterion associated with nonnegative one-step rewards. Assuming that the optimal value function is finite, under mild continuity and compactness restrictions the following result is established: If the number of ergodic classes when a stationary policy is used to drive the system depends continuously on the policy employed, then there exists an optimal stationary policy, extending results obtained by Schal (1984) for risk-neutral dynamic programming. We use results recently established for unichain systems, and analyze the general multichain case via a reduction to a model with the unichain property.
DOI : 10.4064/am28-1-7
Keywords: work concerns markov decision processes finite state space compact action sets decision maker supposed have constant risk sensitivity coefficient control policy graded via risk sensitive expected total reward criterion associated nonnegative one step rewards assuming optimal value function finite under mild continuity compactness restrictions following result established number ergodic classes stationary policy drive system depends continuously policy employed there exists optimal stationary policy extending results obtained schal risk neutral dynamic programming results recently established unichain systems analyze general multichain via reduction model unichain property

Rolando Cavazos-Cadena 1 ; Raul Montes-de-Oca 2

1 Departamento de Estadistica y Calculo Universidad Autonoma Agraria Antonio Narro Buenavista, Saltillo COAH 25315, Mexico
2 Departamento de Matematicas Universidad Autonoma Metropolitana Campus Iztapalapa Avenida Michoacan y La Purisima s//n Col. Vicentina Mexico D.F. 09340, Mexico 
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Rolando Cavazos-Cadena; Raul Montes-de-Oca. Stationary optimal policies in a class
of multichain positive dynamic programs with
finite state space and risk-sensitive criterion. Applicationes Mathematicae, Tome 28 (2001) no. 1, pp. 93-109. doi: 10.4064/am28-1-7

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