Approximation, estimation and control of stochastic systems under a randomized discounted cost criterion

Juan González-Hernández; Raquiel R. López-Martínez; J. Adolfo Minjárez-Sosa

Kybernetika (2009)

  • Volume: 45, Issue: 5, page 737-754
  • ISSN: 0023-5954

Abstract

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The paper deals with a class of discrete-time stochastic control processes under a discounted optimality criterion with random discount rate, and possibly unbounded costs. The state process x t and the discount process α t evolve according to the coupled difference equations x t + 1 = F ( x t , α t , a t , ξ t ) , α t + 1 = G ( α t , η t ) where the state and discount disturbance processes { ξ t } and { η t } are sequences of i.i.d. random variables with densities ρ ξ and ρ η respectively. The main objective is to introduce approximation algorithms of the optimal cost function that lead up to construction of optimal or nearly optimal policies in the cases when the densities ρ ξ and ρ η are either known or unknown. In the latter case, we combine suitable estimation methods with control procedures to construct an asymptotically discounted optimal policy.

How to cite

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González-Hernández, Juan, López-Martínez, Raquiel R., and Minjárez-Sosa, J. Adolfo. "Approximation, estimation and control of stochastic systems under a randomized discounted cost criterion." Kybernetika 45.5 (2009): 737-754. <http://eudml.org/doc/37698>.

@article{González2009,
abstract = {The paper deals with a class of discrete-time stochastic control processes under a discounted optimality criterion with random discount rate, and possibly unbounded costs. The state process $\left\lbrace x_\{t\}\right\rbrace $ and the discount process $\left\lbrace \alpha _\{t\}\right\rbrace $ evolve according to the coupled difference equations $x_\{t+1\}=F(x_\{t\},\alpha _\{t\},a_\{t\},\xi _\{t\}),$$ \alpha _\{t+1\}=G(\alpha _\{t\},\eta _\{t\})$ where the state and discount disturbance processes $\lbrace \xi _\{t\}\rbrace $ and $\lbrace \eta _\{t\}\rbrace $ are sequences of i.i.d. random variables with densities $\rho ^\{\xi \}$ and $\rho ^\{\eta \}$ respectively. The main objective is to introduce approximation algorithms of the optimal cost function that lead up to construction of optimal or nearly optimal policies in the cases when the densities $\rho ^\{\xi \}$ and $\rho ^\{\eta \}$ are either known or unknown. In the latter case, we combine suitable estimation methods with control procedures to construct an asymptotically discounted optimal policy.},
author = {González-Hernández, Juan, López-Martínez, Raquiel R., Minjárez-Sosa, J. Adolfo},
journal = {Kybernetika},
keywords = {discounted cost; random rate; stochastic systems; approximation algorithms; density estimation; density estimation; stochastic systems; discounted cost; random rate; approximation algorithms},
language = {eng},
number = {5},
pages = {737-754},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Approximation, estimation and control of stochastic systems under a randomized discounted cost criterion},
url = {http://eudml.org/doc/37698},
volume = {45},
year = {2009},
}

TY - JOUR
AU - González-Hernández, Juan
AU - López-Martínez, Raquiel R.
AU - Minjárez-Sosa, J. Adolfo
TI - Approximation, estimation and control of stochastic systems under a randomized discounted cost criterion
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 5
SP - 737
EP - 754
AB - The paper deals with a class of discrete-time stochastic control processes under a discounted optimality criterion with random discount rate, and possibly unbounded costs. The state process $\left\lbrace x_{t}\right\rbrace $ and the discount process $\left\lbrace \alpha _{t}\right\rbrace $ evolve according to the coupled difference equations $x_{t+1}=F(x_{t},\alpha _{t},a_{t},\xi _{t}),$$ \alpha _{t+1}=G(\alpha _{t},\eta _{t})$ where the state and discount disturbance processes $\lbrace \xi _{t}\rbrace $ and $\lbrace \eta _{t}\rbrace $ are sequences of i.i.d. random variables with densities $\rho ^{\xi }$ and $\rho ^{\eta }$ respectively. The main objective is to introduce approximation algorithms of the optimal cost function that lead up to construction of optimal or nearly optimal policies in the cases when the densities $\rho ^{\xi }$ and $\rho ^{\eta }$ are either known or unknown. In the latter case, we combine suitable estimation methods with control procedures to construct an asymptotically discounted optimal policy.
LA - eng
KW - discounted cost; random rate; stochastic systems; approximation algorithms; density estimation; density estimation; stochastic systems; discounted cost; random rate; approximation algorithms
UR - http://eudml.org/doc/37698
ER -

References

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Citations in EuDML Documents

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  1. Irina Bashkirtseva, Controlling the stochastic sensitivity in thermochemical systems under incomplete information
  2. Yofre H. García, Juan González-Hernández, Discrete-time Markov control processes with recursive discount rates
  3. Rocio Ilhuicatzi-Roldán, Hugo Cruz-Suárez, Selene Chávez-Rodríguez, Markov decision processes with time-varying discount factors and random horizon
  4. Beatris A. Escobedo-Trujillo, Carmen G. Higuera-Chan, Time-varying Markov decision processes with state-action-dependent discount factors and unbounded costs

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