Before revision: We propose a novel method---based on local moment matching---to approximate the value function of a Markov Decision Process . The method is grounded in recent work by Braverman et al (2020 ) that relates the solution of the Bellman equation to that of a PDE where, in the spirit of the central limit theorem, the transition matrix is reduced to its local first and second moments.
After revision: We propose a novel method---based on local moment matching---to approximate the value function of a Markov Decision Process that stands on two pillars: state aggregation -- as the algorithmic infrastructure; and central-limit-theorem-type approximations -- as the mathematical underpinning of optimality guarantees. The theory is grounded in recent work by Braverman et al (2020 ) that relates the solution of the Bellman equation to that of a PDE where, in the spirit of the central limit theorem, the transition matrix is reduced to its local first and second moments.