A factorization approach to evaluating simultaneous influence diagrams

Evaluating an influence diagram (ID) is a challenging problem because its complexity increases exponentially in the number of decision nodes in the diagram. In this paper, we examine the problem for a special class of IDs where multiple decisions must be made simultaneously. We describe a brief theory that factorizes out the computations common to all policies in evaluating them. Our evaluation approach conducts these computations once and uses them across all policies. We identify the ID structures for which the approach can achieve savings. We show that the approach can be used to efficiently recompute the optimal policy of an ID when its structure or parameters change. Finally, we demonstrate the superior performance of the approach by simulation studies and a military planning example.