Decentralized POMDPs (Dec-POMDPs) are becoming increasingly popular as models for multiagent planning under uncertainty, but solving a Dec-POMDP exactly is known to be an intractable combinatorial optimization problem. In this paper we apply the Cross-Entropy (CE) method, a recently introduced method for combinatorial optimization, to Dec-POMDPs, resulting in a randomized (sampling-based) algorithm for approximately solving Dec-POMDPs. This algorithm operates by sampling
pure policies from an appropriately parametrized stochastic policy, and then evaluates these policies either exactly or approximately in order to define the next stochastic policy to sample from, and so on until
convergence. Experimental results demonstrate that the CE method can search huge spaces efficiently, supporting our claim that combinatorial optimization methods can bring leverage to the approximate solution of Dec-POMDPs.