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1999 | 26 | 3 | 267-280
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
26
Numer
3
Strony
267-280
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-08-04
Twórcy
  • Departamento de Matemáticas, Universidad de Sonora, Rosales s/n Col. Centro, C.P. 83000, Hermosillo, Son., México
Bibliografia
  • [1] D. Blackwell, Discrete dynamic programming, Ann. Math. Statist. 33 (1962), 719-726.
  • [2] E. B. Dynkin and A. A. Yushkevich, Controlled Markov Processes, Springer, New York, 1979.
  • [3] E. I. Gordienko, Adaptive strategies for certain classes of controlled Markov processes, Theory Probab. Appl. 29 (1985), 504-518.
  • [4] E. I. Gordienko and O. Hernández-Lerma, Average cost Markov control processes with weighted norms: existence of canonical policies, Appl. Math. (Warsaw) 23 (1995), 199-218.
  • [5] E. I. Gordienko and J. A. Minjárez-Sosa, Adaptive control for discrete-time Markov processes with unbounded costs: discounted criterion, Kybernetika 34 (1998), no. 2, 217-234.
  • [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.
  • [7] R. Hasminskii and I. Ibragimov, On density estimation in the view of Kolmogorov's ideas in approximation theory, Ann. Statist. 18 (1990), 999-1010.
  • [8] O. Hernández-Lerma, Adaptive Markov Control Processes, Springer, New York, 1989.
  • [9] O. Hernández-Lerma, Infinite-horizon Markov control processes with undiscounted cost criteria: from average to overtaking optimality, Reporte Interno 165, Departamento de Matemáticas, CINVESTAV-IPN, México, 1994.
  • [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.
  • [11] S. A. Lippman, On dynamic programming with unbounded rewards, Manag. Sci. 21 (1975), 1225-1233.
  • [12] P. Mandl, Estimation and control in Markov chains, Adv. Appl. Probab. 6 (1974), 40-60.
  • [13] U. Rieder, Measurable selection theorems for optimization problems, Manuscripta Math. 24 (1978), 115-131.
  • [14] J. A. E. E. Van Nunen and J. Wessels, A note on dynamic programming with unbounded rewards, Manag. Sci. 24 (1978), 576-580.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-zmv26i3p267bwm
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