Deterministic optimal policies for Markov control processes with pathwise constraints

Armando F. Mendoza-Pérez, and Onésimo Hernández-Lerma. "Deterministic optimal policies for Markov control processes with pathwise constraints." Applicationes Mathematicae 39.2 (2012): 185-209. <http://eudml.org/doc/280023>.

@article{ArmandoF2012,
abstract = {This paper deals with discrete-time Markov control processes in Borel spaces with unbounded rewards. Under suitable hypotheses, we show that a randomized stationary policy is optimal for a certain expected constrained problem (ECP) if and only if it is optimal for the corresponding pathwise constrained problem (pathwise CP). Moreover, we show that a certain parametric family of unconstrained optimality equations yields convergence properties that lead to an approximation scheme which allows us to obtain constrained optimal policies as the limit of unconstrained deterministic optimal policies. In addition, we give sufficient conditions for the existence of deterministic policies that solve these constrained problems.},
author = {Armando F. Mendoza-Pérez, Onésimo Hernández-Lerma},
journal = {Applicationes Mathematicae},
keywords = {(discrete-time) Markov control processes; average reward criteria; pathwise average reward; constrained control problems},
language = {eng},
number = {2},
pages = {185-209},
title = {Deterministic optimal policies for Markov control processes with pathwise constraints},
url = {http://eudml.org/doc/280023},
volume = {39},
year = {2012},
}

TY - JOUR
AU - Armando F. Mendoza-Pérez
AU - Onésimo Hernández-Lerma
TI - Deterministic optimal policies for Markov control processes with pathwise constraints
JO - Applicationes Mathematicae
PY - 2012
VL - 39
IS - 2
SP - 185
EP - 209
AB - This paper deals with discrete-time Markov control processes in Borel spaces with unbounded rewards. Under suitable hypotheses, we show that a randomized stationary policy is optimal for a certain expected constrained problem (ECP) if and only if it is optimal for the corresponding pathwise constrained problem (pathwise CP). Moreover, we show that a certain parametric family of unconstrained optimality equations yields convergence properties that lead to an approximation scheme which allows us to obtain constrained optimal policies as the limit of unconstrained deterministic optimal policies. In addition, we give sufficient conditions for the existence of deterministic policies that solve these constrained problems.
LA - eng
KW - (discrete-time) Markov control processes; average reward criteria; pathwise average reward; constrained control problems
UR - http://eudml.org/doc/280023
ER -