Nonparametric adaptive control for discrete-time Markov processes with unbounded costs under average criterion

J. Minjárez-Sosa

Applicationes Mathematicae (1999)

  • Volume: 26, Issue: 3, page 267-280
  • ISSN: 1233-7234

Abstract

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We introduce average cost optimal adaptive policies in a class of discrete-time Markov control processes with Borel state and action spaces, allowing unbounded costs. The processes evolve according to the system equations x t + 1 = F ( x t , a t , ξ t ) , t=1,2,..., with i.i.d. ℝ k -valued random vectors ξ t , which are observable but whose density ϱ is unknown.

How to cite

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Minjárez-Sosa, J.. "Nonparametric adaptive control for discrete-time Markov processes with unbounded costs under average criterion." Applicationes Mathematicae 26.3 (1999): 267-280. <http://eudml.org/doc/219238>.

@article{Minjárez1999,
abstract = {We introduce average cost optimal adaptive policies in a class of discrete-time Markov control processes with Borel state and action spaces, allowing unbounded costs. The processes evolve according to the system equations $x_\{t+1\}=F(x_t,a_t,ξ _t)$, t=1,2,..., with i.i.d. $ℝ^k$-valued random vectors $ξ_t$, which are observable but whose density ϱ is unknown.},
author = {Minjárez-Sosa, J.},
journal = {Applicationes Mathematicae},
keywords = {Markov control process; discounted and average cost criterion; adaptive policy},
language = {eng},
number = {3},
pages = {267-280},
title = {Nonparametric adaptive control for discrete-time Markov processes with unbounded costs under average criterion},
url = {http://eudml.org/doc/219238},
volume = {26},
year = {1999},
}

TY - JOUR
AU - Minjárez-Sosa, J.
TI - Nonparametric adaptive control for discrete-time Markov processes with unbounded costs under average criterion
JO - Applicationes Mathematicae
PY - 1999
VL - 26
IS - 3
SP - 267
EP - 280
AB - We introduce average cost optimal adaptive policies in a class of discrete-time Markov control processes with Borel state and action spaces, allowing unbounded costs. The processes evolve according to the system equations $x_{t+1}=F(x_t,a_t,ξ _t)$, t=1,2,..., with i.i.d. $ℝ^k$-valued random vectors $ξ_t$, which are observable but whose density ϱ is unknown.
LA - eng
KW - Markov control process; discounted and average cost criterion; adaptive policy
UR - http://eudml.org/doc/219238
ER -

References

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  6. [6] E. I. Gordienko and J. A. Minjárez-Sosa, Adaptive control for discrete-time Markov processes with unbounded costs: average criterion, Math. Methods Oper. Res. 48 (1998), 37-55. Zbl0952.90043
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  10. [10] O. Hernández-Lerma and R. Cavazos-Cadena, Density estimation and adaptive control of Markov processes: average and discounted criteria, Acta Appl. Math. 20 (1990), 285-307. Zbl0717.93066
  11. [11] S. A. Lippman, On dynamic programming with unbounded rewards, Manag. Sci. 21 (1975), 1225-1233. Zbl0309.90017
  12. [12] P. Mandl, Estimation and control in Markov chains, Adv. Appl. Probab. 6 (1974), 40-60. Zbl0281.60070
  13. [13] U. Rieder, Measurable selection theorems for optimization problems, Manuscripta Math. 24 (1978), 115-131. Zbl0385.28005
  14. [14] J. A. E. E. Van Nunen and J. Wessels, A note on dynamic programming with unbounded rewards, Manag. Sci. 24 (1978), 576-580. Zbl0374.49015

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