Multiobjective Markov Control Processes: a Linear Programming Approach !
Onésimo Hernández–Lerma, Rosario Romera · 2004
This paper studies discrete-time multiobjective Markov control processes (MCPs) on Borel spaces and unbounded costs. Under mild assumptions, it shows the existence of Pareto policies, which, as in multiobjective optimization problems, are also characterized as optimal policies for a certain class of single-objective (or “scalar”) MCPs. A similar result is obtained for strong Pareto policies, which are Pareto 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 dual program is in fact the same as solving the scalarized MCPs. A multiobjective LQ example illustrates the main results.