1Departamento de Estadistica y Calculo Universidad Autonoma Agraria Antonio Narro Buenavista, Saltillo COAH 25315, Mexico 2Departamento 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
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.
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
Affiliations des auteurs :
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
@article{10_4064_am28_1_7,
author = {Rolando Cavazos-Cadena and Raul Montes-de-Oca},
title = {Stationary optimal policies in a class
of multichain positive dynamic programs with
finite state space and risk-sensitive criterion},
journal = {Applicationes Mathematicae},
pages = {93--109},
year = {2001},
volume = {28},
number = {1},
doi = {10.4064/am28-1-7},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am28-1-7/}
}
TY - JOUR
AU - Rolando Cavazos-Cadena
AU - Raul Montes-de-Oca
TI - Stationary optimal policies in a class
of multichain positive dynamic programs with
finite state space and risk-sensitive criterion
JO - Applicationes Mathematicae
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%A Rolando Cavazos-Cadena
%A Raul Montes-de-Oca
%T Stationary optimal policies in a class
of multichain positive dynamic programs with
finite state space and risk-sensitive criterion
%J Applicationes Mathematicae
%D 2001
%P 93-109
%V 28
%N 1
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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
