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Adaptive control for discrete-time Markov processes with unbounded costs: Average criterion

Author

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  • Evgueni I. Gordienko
  • J. Adolfo Minjárez-Sosa

Abstract

The paper deals with a class of discrete-time Markov control processes with Borel state and action spaces, and possibly unbounded one-stage costs. The processes are given by recurrent 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 whose density ρ is unknown. Assuming observability of ξ t , and taking advantage of the procedure of statistical estimation of ρ used in a previous work by authors, we construct an average cost optimal adaptive policy. Copyright Springer-Verlag Berlin Heidelberg 1998

Suggested Citation

  • Evgueni I. Gordienko & J. Adolfo Minjárez-Sosa, 1998. "Adaptive control for discrete-time Markov processes with unbounded costs: Average criterion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(1), pages 37-55, September.
    • Handle: RePEc:spr:mathme:v:48:y:1998:i:1:p:37-55
    DOI: 10.1007/PL00003993
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    Citations

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    Cited by:

    1. Nadine Hilgert & J. Minjárez-Sosa, 2006. "Adaptive control of stochastic systems with unknown disturbance distribution: discounted criteria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 443-460, July.
    2. Arnoud V. den Boer & Bert Zwart, 2015. "Dynamic Pricing and Learning with Finite Inventories," Operations Research, INFORMS, vol. 63(4), pages 965-978, August.
    3. J. Minjárez-Sosa, 2015. "Markov control models with unknown random state–action-dependent discount factors," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 743-772, October.

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