New Average Optimality Conditions for Semi‐Markov Decision Processes in Borel Spaces

New Average Optimality Conditions for Semi‐Markov Decision Processes in Borel Spaces

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Article ID: iaor20123944
Volume: 153
Issue: 3
Start Page Number: 709
End Page Number: 732
Publication Date: Jun 2012
Journal: Journal of Optimization Theory and Applications
Authors: ,
Keywords: programming: markov decision
Abstract:

This paper deals with semi‐Markov decision processes under the average expected criterion. The state and action spaces are Borel spaces, and the cost/reward function is allowed to be unbounded from above and from below. We give another set of conditions, under which the existence of an optimal (deterministic) stationary policy is proven by a new technique of two average optimality inequalities. Our conditions are slightly weaker than those in the existing literature, and some new sufficient conditions for the verifications of our assumptions are imposed on the primitive data of the model. Finally, we illustrate our results with three examples.

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