Existence of optimal stationary policies in finite dynamic programs with nonnegative rewards – an alternative approach

Existence of optimal stationary policies in finite dynamic programs with nonnegative rewards – an alternative approach

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Article ID: iaor20023453
Country: United States
Volume: 15
Issue: 4
Start Page Number: 557
End Page Number: 564
Publication Date: Jan 2001
Journal: Probability in the Engineering and Informational Sciences
Authors: ,
Keywords: markov processes
Abstract:

This article concerns Markov decision chains with finite state and action spaces, and a control policy is graded via the expected total-reward criterion associated to a nonnegative reward function. Within this framework, a classical theorem guarantees the existence of an optimal stationary policy whenever the optimal value function is finite, a result that is obtained via a limit process using the discounted criterion. The objective of this article is to present an alternative approach, based entirely on the properties of the expected total-reward index, to establish such an existence result.

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