Standard dynamic programming applied to time aggregated Markov decision processes

In this note we address the time aggregation approach to ergodic finite state Markov decision processes with uncontrollable states. We propose the use of the time aggregation approach as an intermediate step toward constructing a transformed MDP whose state space is comprised solely of the controllable states. The proposed approach simplifies the iterative search for the optimal solution by eliminating the need to define an equivalent parametric function, and results in a problem that can be solved by simpler, standard MDP algorithms.