In a recent paper, Lippman presents sufficient conditions for Denardo's N-stage contraction in discounted semi-Markov decision processes with unbounded rewards. In this note it is demonstrated that Lippman's conditions may be replaced by weaker conditions which even imply l-stage contraction. The verification of the conditions of this note is somewhat easier.

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van Nunen, J., & Wessels, J. (1978). A Note on Dynamic Programming with Unbounded Rewards. Management Science, 24(5), 576–580. Retrieved from