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 and the discount process evolve according to the coupled difference equations where the state and discount disturbance processes and are sequences of i.i.d. random variables with densities and 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 and 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. Rocio Ilhuicatzi-Roldán, Hugo Cruz-Suárez, Selene Chávez-Rodríguez, Markov decision processes with time-varying discount factors and random horizon
  3. Yofre H. García, Juan González-Hernández, Discrete-time Markov control processes with recursive discount rates
  4. Beatris A. Escobedo-Trujillo, Carmen G. Higuera-Chan, Time-varying Markov decision processes with state-action-dependent discount factors and unbounded costs
  5. E. Everardo Martinez-Garcia, J. Adolfo Minjárez-Sosa, Oscar Vega-Amaya, Partially observable Markov decision processes with partially observable random discount factors

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