We study the first-passage problem with multiple costs. We characterize an optimal deterministic stationary policy via the systems of linear inequalities and present a policy iteration algorithm for finding all optimal deterministic stationary policies. The algorithm is illustrated by a...

For a vector-valued Markov decision process with discounted reward criterion, we study the structure of its value spaces defined for all initial states. At first we discuss the relationship between the value spaces, i.e. we verify a linking property for optimality. We next show that if the...

For a vector-valued Markov decision process with discounted reward criterion, we study the structure of its value spaces defined for all initial states. At first we discuss the relationship between the value spaces, i.e. we verify a linking property for optimality. We next show that if the...

We study a multi-objective shortest path problem. We formulate a multi-objective Markov decision process model for the problem and solve it by the policy improvement procedure. We first show by counter-examples the differences between the multi-objective shortest path problem and the...

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...