Formulating asymmetric decision problems as decision circuits

Abstract

Decision analysis problems have traditionally been solved using either decision trees or influence diagrams. Although decision trees are better at handling asymmetry, prevalent in many reliability and risk analysis problems, influence diagrams can solve larger real-world problems by exploiting conditional independence. Decision circuits are graphical representations that combine the computational benefits of both graphical models. They are syntactic representations, i.e., they depict the summation, multiplication, and maximization operations required to solve a decision analysis problem. Previous work on decision circuits has focused on compiling them automatically from influence diagrams and describing the ways in which they can be used for efficient solution and sensitivity analysis. In this paper, we show how a decision circuit can be formulated directly, with or without the preprocessing of numbers that are assessed from the decision maker. By constructing two decision circuits for a nuclear reactor example, one using probabilities in inferred form and the other using probabilities in assessed form, we show how decision circuits generalize decision trees. The notion of coalescence is also made more explicit because computations for decision analysis can be saved and then reused in several ways. Because of their generality, decision circuits provide the analyst with a great deal of flexibility in problem formulation. ©2012 INFORMS.