Transient policies in discrete dynamic programming: Linear programming including suboptimality tests and additional constraints

This paper investigates the computation of transient-optimal policies in discrete dynamic programming. The model, is quite general: it may contain transient as well as nontransient policies. and the transition matrices are not necessarily substochastic. A functional equation for the so-called transient-value-vector is derived and the concept of superharmonicity is introduced. This concept provides the linear program to compute the transientvalue-vector and a transient-optimal policy. We also discuss the elimination of suboptimal actions, the solution of problems with additional constraints, and the computation of an efficient policy for a multiple objective dynamic programming problem.