Skip to main content
Log in

Non-randomized strategies in stochastic decision processes

  • Borel State Space
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

This paper deals with discrete time infinite horizon stochastic decision processes with various reward criteria. Sufficient conditions are obtained for the value of a class of strategies to be equal to the value of the subclass of non-randomized strategies from this class.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R.J. Aumann, Mixed and behavior strategies in infinite extensive games, Ann. Math. Studies 53 (1964) 627–650.

    Google Scholar 

  2. D.P. Bertsekas and S.E. Shreve,Stochastic Optimal Control: The Discrete Time Case (Academic Press, New York, 1978).

    Google Scholar 

  3. D. Blackwell, D. Freedman and M. Orkin, The optimal reward operator in dynamic programming, Ann. Statist. 1 (1974) 926–941.

    Google Scholar 

  4. E.B. Dynkin and A.A. Yushkevich,Controlled Markov Processes (Springer, New York, 1979).

    Google Scholar 

  5. E.A. Feinberg, Non-randomized Markov and semi-Markov strategies in dynamic programming, Theory Probab. Appl. 27 (1982) 116–126.

    Google Scholar 

  6. E.A. Feinberg, Controlled Markov processes with arbitrary numerical criteria, Theory Probab. Appl. 27 (1982) 486–503.

    Google Scholar 

  7. E.A. Feinberg, Sufficient classes of strategies in discrete dynamic programming I: Decomposition of randomized strategies and embedded models, Theory Probab. Appl. 31 (1986) 658–668.

    Google Scholar 

  8. E.A. Feinberg, On stationary strategies in Borel dynamic programming, submitted to Math. Oper. Res. (1989).

  9. E.A. Feinberg and I.M. Sonin, Persistently nearly optimal strategies in stochastic dynamic programming, in:Statistics and Control of Stochastic Processes (Steklov Seminar, 1984), Optimization Software, New York (1985) pp. 69–101.

    Google Scholar 

  10. I.I. Gikhman and A.V. Skorokhod,Controlled Random Processes (Springer, New York, 1979).

    Google Scholar 

  11. K.M. van Hee, Markov strategies in dynamic programming, Math. Oper. Res. 3 (1978) 37–41.

    Google Scholar 

  12. T.P. Hill, On the existence of good Markov strategies, Trans. Amer. Math. Soc. 247 (1979) 157–176.

    Google Scholar 

  13. T.P. Hill and V.C. Pestien, The existence of good Markov strategies for decision processes with general payoffs, Stochastic Process. Appl. 24 (1987) 61–76.

    Google Scholar 

  14. G. Kallianpur,Stochastic Filtering Theory (Springer, New York, 1980).

    Google Scholar 

  15. N.V. Krylov, The construction of an optimal strategy for a finite controlled chain, Theory Probab. Appl. 10 (1965) 45–54.

    Google Scholar 

  16. P.A. Meyer,Probability and Potentials (Blaisdell, Waltham, MA, 1966).

    Google Scholar 

  17. J. Neveu,Mathematical Foundations of the Calculus of Probability (Holden-Day, San Francisco, 1965).

    Google Scholar 

  18. M. Schäl, Stationary policies in dynamic programming models under compactness assumptions, Math. Oper. Res. 8 (1983) 366–372.

    Google Scholar 

  19. A.N. Shiryaev,Optimal Stopping Rules (Springer, New York, 1978).

    Google Scholar 

  20. I.M. Sonin and E.A. Feinberg, Sufficient classes of strategies in controllable countable Markov chains with total criterion, Sov. Math. Dokl. 29 (1984) 308–311.

    Google Scholar 

  21. R. Strauch, Negative dynamic programming, Ann. Math. Statist. 37 (1966) 871–890.

    Google Scholar 

  22. J. van der Wal,Stochastic Dynamic Programming (Mathematisch Centrum, Amsterdam, 1981).

    Google Scholar 

  23. A.A. Yushkevich and R.J. Chitashvili, Controlled random sequences, Russian Math. Surveys 37 (1982) 239–274.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Feinberg, E.A. Non-randomized strategies in stochastic decision processes. Ann Oper Res 29, 315–332 (1991). https://doi.org/10.1007/BF02283603

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02283603

Keywords

Navigation