Computing Optimal Stationary Policies for Multi-Objective Markov Decision Processes

Abstract

This paper describes a novel algorithm called CON-MODP for computing Pareto optimal policies for deterministic multi-objective sequential decision problems. CON-MODP is a value iteration based multi-objective dynamic programming algorithm that only computes stationary policies. We observe that for guaranteeing convergence to the unique Pareto optimal set of deterministic stationary policies, the algorithm needs to perform a policy evaluation step on particular policies that are inconsistent in a single state that is being expanded. We prove that the algorithm converges to the Pareto optimal set of value functions and policies for deterministic infinite horizon discounted multi-objective Markov decision processes. Experiments show that CON-MODP is much faster than previous multi-objective value iteration algorithms.