A simple condition for regularity in negative programming

Abstract

A simple condition (the ‘bridging condition') is given for a Markov decision problem with non-negative costs to enjoy the regularity properties enunciated in Theorem 1. The bridging condition is sufficient for regularity, and is not far from being necessary, in a sense explained in Section 2. In Section 8 we consider the different classes of terminal loss functions (domains of attraction) associated with different solutions of (14). Some conjectures concerning these domains of attraction are either proved, or disproved by counter-example.