Approximate Modified Policy Iteration

Modified policy iteration (MPI) is a dynamic programming (DP) algorithm that contains the two celebrated policy and value iteration methods. Despite its generality, MPI has not been thoroughly studied, especially its approximation form which is used when the state and/or action spaces are large or infinite. In this paper, we propose three implementations of approximate MPI (AMPI) that are extensions of well-known approximate DP algorithms: fitted-value iteration, fittedQ iteration, and classification-based policy iteration. We provide error propagation analysis that unifies those for approximate policy and value iteration. For the classificationbased implementation, we develop a finitesample analysis that shows that MPI’s main parameter allows to control the balance between the estimation error of the classifier and the overall value function approximation.