On Local Computations of Influence Diagrams

Influence diagrams (IDs) are compact and intuitive models for representation and analysis of decision problems under uncertainty. Influence diagrams have always been imposed on no-forgetting and regularity constraints which guarantee that global optimal strategy can be solved successively by local computations on each decision nodes according to a solution ordering. However, it is difficult to solve the global optimal strategy influence diagrams relaxing these two fundamental assumptions, known as limited memory influence diagrams (LIMIDs), because optimal strategy may be found only if all possible strategies have been evaluated. And influence diagrams may not imply any solution ordering. This paper tries to achieve a lower complexity of computations by capturing the graphical characterizations of local computations in Influence diagrams. The definition of the solution ordering is extended from among decision variables to among the sets of decision variables, and extremal sets are presented. Moreover, the global optimal strategy can be found locally on extremal sets. Thus, influence diagrams may be solved successively by local computations on minimal extremal sets even if influence diagrams do not imply any exact solution order among decision variables. And an improvement for solving algorithms would be achieved.