Efficient policies for the problem of optimal node visitation in acyclic stochastic digraphs

Given a stochastic, acyclic, connected digraph with a single source node and a control agent that repetitively traverses this graph, each time starting from the source node, we want to define a control policy that will enable this agent to visit each of the graph terminal nodes a prespecified number of times, while minimizing the expected number of the graph traversals. In previous work, we formulated this problem as a specially structured Discrete Time Markov Decision Process, and we developed an asymptotically optimal randomized policy. In this work, we develop improved policies by exploiting the special structure of the problem and the relevant theory of suboptimal control.