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...

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...