A Computational Theory of Decision Networks

Decision trees (Raiffa 1968) are the first paradigm where an agent can deal with multiple decisions. The non-forgetting influence diagram formalism (Howard and Matheson 1983, Shachter 1986) improves decision trees by exploiting random variables'' independencies of decision variables and other random variables. In this paper, we introduce a notion of decision networks that further explore decision variables'' independencies of random variables and other decision variables. We also drop the semantic constraints of total ordering of decisions and of one value node. Only the fundamental constraint of acyclicity is kept. \par From a computational point of view, it is desirable if a decision network is stepwise-solvable, i.e if it can be evaluated by considering one decision at a time. However, decision network in the most general sense need not to be stepwise-solvable. A syntactic constraint called stepwise-decomposability is therefore imposed. We show that stepwise-decomposable decision networks can be evaluated not only by considering one decision at a time, but also by considering one portion of the network at a time.