Approximate Receding Horizon Approach for Markov Decision Processes: Average Reward Case

We consider an approximation scheme for solving Markov Decision Processes (MDPs) with countable state space, finite action space, and bounded rewards that uses an approximate solution of a fixed finite-horizon sub-MDP of a given infinite-horizon MDP to create a stationary policy, which we call “approximate receding horizon control”. We first analyze the performance of the approximate receding horizon control for infinite-horizon average reward under an ergodicity assumption, which also generalizes the result obtained by White [36]. We then study two examples of the approximate receding horizon control via lower bounds to the exact solution to the sub-MDP. The first control policy is based on a finite-horizon approximation of Howard’s policy improvement of a single policy and the second policy is based on a generalization of the single policy improvement for multiple policies. Along the study, we also provide a simple alternative proof on the policy improvement for countable state space. We finally discuss practical implementations of these schemes via simulation.