Pareto optimality in multiobjective Markov control processes

This paper studies discrete-time multiobjective Markov control processes (MCPs) on Borel spaces and with unbounded costs. Under mild assumptions, it shows the existence of Pareto optimal control policies, which are also characterized as optimal policies for a certain class of single-objective ( or "scalar") MCPs. A similar result is obtained for strong Pareto optimal policies, which are Pareto optimal policies whose cost vector is the closest, in the Euclidean norm, to the virtual minimum. To obtain these results, the basic idea is to transform the multiobjective MCP into an equivalent multiobjective measure problem (MMP). In addition, MMP is restated as a primal multiobjective linear program and it is shown that solving the scalarized MCPs is in fact the same as solving the dual of MMP. A multiobjective LQ example illustrates the main results