Stationary optimal policies in a class of multichain positive dynamic programs with finite state space and risk-sensitive criterion

Rolando Cavazos-Cadena, and 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 28.1 (2001): 93-109. <http://eudml.org/doc/279817>.

@article{RolandoCavazos2001,
abstract = {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.},
author = {Rolando Cavazos-Cadena, Raul Montes-de-Oca},
journal = {Applicationes Mathematicae},
keywords = {Markov decision processes; risk-sensitive optimality; stationary policy; utility function; structural stability; ergodic class; invariant distribution},
language = {eng},
number = {1},
pages = {93-109},
title = {Stationary optimal policies in a class of multichain positive dynamic programs with finite state space and risk-sensitive criterion},
url = {http://eudml.org/doc/279817},
volume = {28},
year = {2001},
}

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
PY - 2001
VL - 28
IS - 1
SP - 93
EP - 109
AB - 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.
LA - eng
KW - Markov decision processes; risk-sensitive optimality; stationary policy; utility function; structural stability; ergodic class; invariant distribution
UR - http://eudml.org/doc/279817
ER -