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...

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...

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...