Characterization of Optimal Policies in Vector-Valued Markovian Decision Processes

Abstract
Infinite horizon Markovian decision processes with Rp-valued additive utilities are considered. The optimization criterion, here, is a pseudo-order preference relation induced by a convex cone in Rp. The state space is a countable set, and the action space is a compact metric space. Certain assumptions on the continuity of the reward vector and the transition probability are made. In this setting, an algorithm improving policies with respect to the chosen preference relation is given. A point-to-set mapping is defined, and optimal policies are characterized by fixed points of the mapping which are maximal in the set of all fixed points.

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