Computation of weighted sums of rewards for concurrent MDPs

We consider sets of Markov decision processes (MDPs) with shared state and action spaces and assume that the individual MDPs in such a set represent different scenarios for a system's operation. In this setting, we solve the problem of finding a single policy that performs well under each of these scenarios by considering the weighted sum of value vectors for each of the scenarios. Several solution approaches as well as the general complexity of the problem are discussed and algorithms that are based on these solution approaches are presented. Finally, we compare the derived algorithms on a set of benchmark problems.