Sum-Product-Max Networks for Tractable Decision Making

Investigations into probabilistic graphical models for decision making have predominantly centered on influence diagrams (IDs) and decision circuits (DCs) for representation and computation of decision rules that maximize expected utility. Since IDs are typically handcrafted and DCs are compiled from IDs, in this paper we propose an approach to learn the structure and parameters of decision-making problems directly from data. We present a new representation called sum-product-max network (SPMN) that generalizes a sum-product network (SPN) to the class of decision-making problems and whose solution, analogous to DCs, scales linearly in the size of the network. We show that SPMNs may be reduced to DCs linearly and present a first method for learning SPMNs from data. This approach is significant because it facilitates a novel paradigm of tractable decision making driven by data.