Optimal Decomposition of Limited Memory Influence Diagrams

Complexity of solving influence diagrams increases exponentially in the number of decision variables. In Limited Memory Influence Diagrams (LIMIDs), some decisions must be made simultaneously and cooperatively and some may be independent of others. This paper partitions decision variables into different classes by an equivalent relation which decision variables in one class are dependent of each other, and two decisions contained in two different classes can be made independently. Moreover, relevant variables over classes of decision variables are defined. Then, based on relevant variables and requisite observations, influence diagrams can be decomposed into multiple local models, one of which consists of a class of decision variables and its requisite parents and relevant variables. Once influence diagrams have been decomposed, the optimal strategy can be determined by sub-strategies which can be found in sub-models independently.