In this paper we are concerned with the vector-valued Markov decision process and consider 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...

For a vector-valued Markov decision process, we characterize optimal (deterministic) stationary policies by systems of linear inequalities and present an algorithm for finding all optimal stationary policies from among all randomized, history-remembering ones. The algorithm consists of improving...