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Some Bounds for Discounted Sequential Decision Processes

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  • Evan L. Porteus

    (Stanford University)

Abstract

New bounds are obtained on the optimal return function for what are called discounted sequential decision processes. Such processes are equivalent to ones satisfying the contraction and monotonicity properties (Denardo [Denardo, E. V., 1967. Contraction mappings in the theory underlying dynamic programming. SIAM Review. Vol. 9, pp. 165-177.]). The bounds are useful primarily in the infinite horizon case. Certain subprocesses are exploited, based on the simple notion of taking only those states which are relevant into consideration. Some existing algorithms and some of their obvious extensions are listed. The possibility of identifying nonoptimal decisions, as in MacQueen [MacQueen, J. B., 1966. A Modified dynamic programming method for markovian decision problems. Journal of Mathematical Analysis and Applications. Vol. 14, pp. 38-43.], is included.

Suggested Citation

  • Evan L. Porteus, 1971. "Some Bounds for Discounted Sequential Decision Processes," Management Science, INFORMS, vol. 18(1), pages 7-11, September.
    • Handle: RePEc:inm:ormnsc:v:18:y:1971:i:1:p:7-11
    DOI: 10.1287/mnsc.18.1.7
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    Cited by:

    1. Paul Zipkin, 2008. "Old and New Methods for Lost-Sales Inventory Systems," Operations Research, INFORMS, vol. 56(5), pages 1256-1263, October.
    2. Eric A. Hansen, 2017. "Error bounds for stochastic shortest path problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 1-27, August.
    3. Herzberg, Meir & Yechiali, Uri, 1996. "A K-step look-ahead analysis of value iteration algorithms for Markov decision processes," European Journal of Operational Research, Elsevier, vol. 88(3), pages 622-636, February.
    4. Pelin Canbolat & Uriel Rothblum, 2013. "(Approximate) iterated successive approximations algorithm for sequential decision processes," Annals of Operations Research, Springer, vol. 208(1), pages 309-320, September.
    5. Julio L. Ortiz, 2022. "Spread Too Thin: The Impact of Lean Inventories," International Finance Discussion Papers 1342, Board of Governors of the Federal Reserve System (U.S.).
    6. Seow, Hsin-Vonn & Thomas, Lyn C., 2006. "Using adaptive learning in credit scoring to estimate take-up probability distribution," European Journal of Operational Research, Elsevier, vol. 173(3), pages 880-892, September.

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