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Adaptive policies for time-varying stochastic systems under discounted criterion

Author

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  • Nadine Hilgert
  • J. Adolfo Minjárez-Sosa

Abstract

We consider a class of time-varying stochastic control systems, with Borel state and action spaces, and possibly unbounded costs. The processes evolve according to a discrete-time equation x n + 1 =G n (x n , a n , ξ n ), n=0, 1, … , where the ξ n are i.i.d. ℜ k -valued random vectors whose common density is unknown, and the G n are given functions converging, in a restricted way, to some function G ∞ as n→∞. Assuming observability of ξ n , we construct an adaptive policy which is asymptotically discounted cost optimal for the limiting control system x n+1 =G ∞ (x n , a n , ξ n ). Copyright Springer-Verlag Berlin Heidelberg 2001

Suggested Citation

  • Nadine Hilgert & J. Adolfo Minjárez-Sosa, 2001. "Adaptive policies for time-varying stochastic systems under discounted criterion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(3), pages 491-505, December.
    • Handle: RePEc:spr:mathme:v:54:y:2001:i:3:p:491-505
    DOI: 10.1007/s001860100170
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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. 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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