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On dynamic programming: Compactness of the space of policies

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  • Schäl, Manfred

Abstract

The compactness of the set of policies in a dynamic programming decision model, which guarantees the existence of an optimal policy, is proven by reducing the problem to the compactness of the set of probability measures which are induced by the policies. When studying the set of probability measures, use is made of the weak topology and the so-called ws[infinity]-topology. A definition and a discussion of the latter topology is given in this paper, where we pay attention to criteria for relative compactness.

Suggested Citation

  • Schäl, Manfred, 1975. "On dynamic programming: Compactness of the space of policies," Stochastic Processes and their Applications, Elsevier, vol. 3(4), pages 345-364, October.
    • Handle: RePEc:eee:spapps:v:3:y:1975:i:4:p:345-364
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    Cited by:

    1. Jaśkiewicz, Anna & Matkowski, Janusz & Nowak, Andrzej S., 2011. "Persistently optimal policies in stochastic dynamic programming with generalized discounting," MPRA Paper 31755, University Library of Munich, Germany.

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