Approximate Linear-Programming Algorithms for Graph-Based Markov Decision Processes

In this article, we consider a form of compact representation of MDP based on graphs, and we propose an approximate solution algorithm derived from this representation. The approach we propose belongs to the family of Approximate Linear Programming methods, but the graph-structure we assume allows it to become particularly efficient. The proposed method complexity is linear in the number of variables in the graph and only exponential in the width of a dependency graph among variables.