Time-varying Markov decision processes with state-action-dependent discount factors and unbounded costs

Escobedo-Trujillo, Beatris A., and Higuera-Chan, Carmen G.. "Time-varying Markov decision processes with state-action-dependent discount factors and unbounded costs." Kybernetika 55.1 (2019): 166-182. <http://eudml.org/doc/294596>.

@article{Escobedo2019,
abstract = {In this paper we are concerned with a class of time-varying discounted Markov decision models $\mathcal \{M\}_n$ with unbounded costs $c_n$ and state-action dependent discount factors. Specifically we study controlled systems whose state process evolves according to the equation $x_\{n+1\}=G_n(x_n,a_n,\xi _n), n=0,1,\ldots $, with state-action dependent discount factors of the form $\alpha _n(x_n,a_n)$, where $a_n$ and $\xi _n$ are the control and the random disturbance at time $n$, respectively. Assuming that the sequences of functions $\lbrace \alpha _n\rbrace $,$\lbrace c_n\rbrace $ and $\lbrace G_n\rbrace $ converge, in certain sense, to $\alpha _\infty $, $c_\infty $ and $G_\infty $, our objective is to introduce a suitable control model for this class of systems and then, to show the existence of optimal policies for the limit system $\mathcal \{M\}_\infty $ corresponding to $\alpha _\infty $, $c_\infty $ and $G_\infty $. Finally, we illustrate our results and their applicability in a class of semi-Markov control models.},
author = {Escobedo-Trujillo, Beatris A., Higuera-Chan, Carmen G.},
journal = {Kybernetika},
keywords = {discounted optimality; non-constant discount factor; time-varying Markov decision processes},
language = {eng},
number = {1},
pages = {166-182},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Time-varying Markov decision processes with state-action-dependent discount factors and unbounded costs},
url = {http://eudml.org/doc/294596},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Escobedo-Trujillo, Beatris A.
AU - Higuera-Chan, Carmen G.
TI - Time-varying Markov decision processes with state-action-dependent discount factors and unbounded costs
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 1
SP - 166
EP - 182
AB - In this paper we are concerned with a class of time-varying discounted Markov decision models $\mathcal {M}_n$ with unbounded costs $c_n$ and state-action dependent discount factors. Specifically we study controlled systems whose state process evolves according to the equation $x_{n+1}=G_n(x_n,a_n,\xi _n), n=0,1,\ldots $, with state-action dependent discount factors of the form $\alpha _n(x_n,a_n)$, where $a_n$ and $\xi _n$ are the control and the random disturbance at time $n$, respectively. Assuming that the sequences of functions $\lbrace \alpha _n\rbrace $,$\lbrace c_n\rbrace $ and $\lbrace G_n\rbrace $ converge, in certain sense, to $\alpha _\infty $, $c_\infty $ and $G_\infty $, our objective is to introduce a suitable control model for this class of systems and then, to show the existence of optimal policies for the limit system $\mathcal {M}_\infty $ corresponding to $\alpha _\infty $, $c_\infty $ and $G_\infty $. Finally, we illustrate our results and their applicability in a class of semi-Markov control models.
LA - eng
KW - discounted optimality; non-constant discount factor; time-varying Markov decision processes
UR - http://eudml.org/doc/294596
ER -