Solution Methods for Decision Graphs

In Chapter 9 we presented graphical languages for modeling decision problems. The languages ease the burden of specifying the problem and transfer the complexity of the problem to the computer. For problems with a finite time horizon, the computer may fold out the specification to a decision tree and determine an optimal strategy by averaging out and folding back as described in Section 9.3.3. However, the calculations may be intractable, and in this chapter we present alternative methods exploiting symmetries in the decision problem. Sections 10.1–10.3 are devoted to solution methods for influence diagrams. Section 10.4 presents a method for solving unconstrained influence diagrams. In Section 10.5 we consider decision theoretic troubleshooting, which has next to no temporal ordering, and for which the decision trees tend to be intractably large. In Section 10.6 we present two methods for solving MDPs, and a method for solving POMDPs is indicated. The last section presents LIMIDs, which is a way of approximating influence diagrams by limiting the memory of the decision maker.