Optimizing mixtures of dependency trees with application to distributed probabilistic control

One of the problems in distributed control is that of establishing a communication network topology between the intervening controllers that best suits the closed loop performance of the whole system. In this paper, a particular view of this problem is analyzed where the optimal actuation is described probabilistically and assumed to be jointly specified. The main problem is that of finding a topology having pairwise communication links that best approaches a joint distribution of actions at each time instant. The proposed algorithm uses properties of the natural gradient in the manifold of categorical distributions to find a mixture of dependency trees under certain network topology constraints.