Absorbing Markov Decision Processes

TL;DR

This paper investigates the properties of absorbing Markov Decision Processes with measurable state and action spaces, providing conditions for solutions to be occupation measures and characterizing these measures through the characteristic equation.

Contribution

It offers new necessary and sufficient conditions ensuring solutions to the characteristic equation are occupation measures in absorbing MDPs.

Findings

Solutions to the characteristic equation may not always be occupation measures.

Occupation measures form a compact set under certain continuity-compactness conditions.

Characterization of occupation measures via the characteristic equation and additional conditions.

Abstract

In this paper, we study discrete-time absorbing Markov Decision Processes (MDP) with measurable state space and Borel action space with a given initial distribution. For such models, solutions to the characteristic equation that are not occupation measures may exist. Several necessary and sufficient conditions are provided to guarantee that any solution to the characteristic equation is an occupation measure. Under the so-called continuity-compactness conditions, it is shown that the set of occupation measures is compact in the weak-strong topology if and only if the model is uniformly absorbing. Finally, it is shown that the occupation measures are characterized by the characteristic equation and an additional condition. Several examples are provided to illustrate our results.