Approximation and estimation in Markov control processes under a discounted criterion

J. Adolfo Minjárez-Sosa

Kybernetika (2004)

  • Volume: 40, Issue: 6, page [681]-690
  • ISSN: 0023-5954

Abstract

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We consider a class of discrete-time Markov control processes with Borel state and action spaces, and ℜ k -valued i.i.d. disturbances with unknown density ρ . Supposing possibly unbounded costs, we combine suitable density estimation methods of ρ with approximation procedures of the optimal cost function, to show the existence of a sequence { f ^ t } of minimizers converging to an optimal stationary policy f ∞ .

How to cite

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Minjárez-Sosa, J. Adolfo. "Approximation and estimation in Markov control processes under a discounted criterion." Kybernetika 40.6 (2004): [681]-690. <http://eudml.org/doc/33728>.

@article{Minjárez2004,
abstract = {We consider a class of discrete-time Markov control processes with Borel state and action spaces, and $\Re ^\{k\}$-valued i.i.d. disturbances with unknown density $\rho .$ Supposing possibly unbounded costs, we combine suitable density estimation methods of $\rho $ with approximation procedures of the optimal cost function, to show the existence of a sequence $\lbrace \hat\{f\}_\{t\}\rbrace $ of minimizers converging to an optimal stationary policy $f_\{\infty \}.$},
author = {Minjárez-Sosa, J. Adolfo},
journal = {Kybernetika},
keywords = {Markov control processes; density estimation; discounted cost criterion; Markov control process; density estimation; discounted cost criterion},
language = {eng},
number = {6},
pages = {[681]-690},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Approximation and estimation in Markov control processes under a discounted criterion},
url = {http://eudml.org/doc/33728},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Minjárez-Sosa, J. Adolfo
TI - Approximation and estimation in Markov control processes under a discounted criterion
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 6
SP - [681]
EP - 690
AB - We consider a class of discrete-time Markov control processes with Borel state and action spaces, and $\Re ^{k}$-valued i.i.d. disturbances with unknown density $\rho .$ Supposing possibly unbounded costs, we combine suitable density estimation methods of $\rho $ with approximation procedures of the optimal cost function, to show the existence of a sequence $\lbrace \hat{f}_{t}\rbrace $ of minimizers converging to an optimal stationary policy $f_{\infty }.$
LA - eng
KW - Markov control processes; density estimation; discounted cost criterion; Markov control process; density estimation; discounted cost criterion
UR - http://eudml.org/doc/33728
ER -

References

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  9. Hernández-Lerma O., Lasserre J. B., Discrete-Time Markov Control Processes: Basic Optimality Criteria, Springer–Verlag, New York 1996 Zbl0840.93001MR1363487
  10. Hernández-Lerma O., Lasserre J. B., Further Topics on Discrete-Time Markov Control Processes, Springer–Verlag, New York 1999 Zbl0928.93002MR1697198
  11. Hernández-Lerma O., Marcus S. I., 10.1016/0167-6911(87)90055-7, Systems Control Lett. 9 (1987), 307–315 (1987) Zbl0637.93075MR0912683DOI10.1016/0167-6911(87)90055-7
  12. Hilgert N., Minjárez-Sosa J. A., 10.1007/s001860100170, Math. Methods Oper. Res. 54 (2001), 491–505 Zbl1042.93065MR1890916DOI10.1007/s001860100170
  13. Schäl M., 10.1007/BF00532612, Z. Wahrs. Verw. Gerb. 32 (1975), 179–196 (1975) MR0378841DOI10.1007/BF00532612

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