Optimal stationary policies in the vector-valued Markov decision process

This paper is concerned with the vector-valued Markov decision process and considers the characterization of optimal stationary policies among the set of all (randomized, history-dependent) policies. Using the scalarization technique developed for the vector maximizing problem in the nonlinear programming, it presents a necessary condition and a (different) sufficient condition for a statinary policy to be optimal among the set of all policies.