Compactness of the space of non-randomized policies in countable-state sequential decision processes

Compactness of the space of non-randomized policies in countable-state sequential decision processes

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Article ID: iaor20103314
Volume: 71
Issue: 2
Start Page Number: 307
End Page Number: 323
Publication Date: Apr 2010
Journal: Mathematical Methods of Operations Research
Authors: ,
Abstract:

For sequential decision processes with countable state spaces, we prove compactness of the set of strategic measures corresponding to nonrandomized policies. For the Borel state case, this set may not be compact in spite of compactness of the set of strategic measures corresponding to all policies. We use the compactness result from this paper to show the existence of optimal policies for countable-state constrained optimization of expected discounted and nonpositive rewards, when the optimality is considered within the class of nonrandomized policies. This paper also studies the convergence of a value-iteration algorithm for such constrained problems.

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