Optimal Fixed-Size Controllers for Decentralized POMDPs

Solving decentralized partially observable Markov decision processes (DEC-POMDPs) is a difficult task. Exact solutions are intractable in all but the smallest problems and approximate solutions provide limited optimality guarantees. As a more principled alternative, we present a novel formulation of an optimal fixed-size solution of a DEC-POMDP as a nonlinear program. We discuss the benefits of this representation and evaluate several optimization methods. While the methods used in this paper only guarantee locally optimal solutions, a wide range of powerful nonlinear optimization techniques may now be applied to this problem. We show that by using our formulation in various domains, solution quality is higher than a current state-of-the-art approach. These results show that optimization can be used to provide high quality solutions to DEC-POMDPs while maintaining moderate memory and time usage.