On functional equations for Kth best policies in Markov decision processes

초록

This paper revisits the problem of finding the values of Kth best policies for finite-horizon finite Markov decision processes. The recursive dynamic-programming (DP) equations established by Bellman and Kalaba for non-deterministic MDPs with zero-cost function in [Bellman, R., & Kalaba, R. (1960). On kth best policies. Journal of SIAM, 8,582-588] are incomplete because expectation and selection for the Kth minimum do not interchange in general. Based on the DP equations by Dreyfus for the Kth shortest path problem, some non-DP equations generally satisfied by the values of the Kth best policies are identified, from which corrected Bellman and Kalaba's DP equations are derived with an appropriate sufficient condition. (C) 2012 Elsevier Ltd. All rights reserved.

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