Brief Introduction to Some Simple Classes: Solving Influence Diagrams
From DSL
SMILE provides full support for influence diagrams, including multiple decision nodes and multiple value nodes. When the network is updated, the expected utility of each of the policies will be calculated.
Temporal Order
It is required that all the decision nodes be ordered in time. If this is not the case, updating beliefs will create the necessary temporal links in an arbitrary manner.
Global Utility
If multiple utility nodes are used, for solving the model it is necessary to have a global utility node that merges all the preferences. If there is no such global node, the library will automatically assume that the global utility is linearly additive and that all utility nodes have the same weight and will add their values together in order to obtain the global utility.
Indexing Parents
The results for each node will be indexed by its indexing parents. These indexing parents are the decision nodes and informational predecessors of decision nodes that are d-connected to the given node. A node is d-connected if it is not d-separated.
Interpreting the Results
In single utility node networks, the value of the utility node will contain the expected utility for each policy. In multiple utility nodes networks, the value of each utility node will contain the expected utility for each of the policies of the decision nodes that contribute to it (as there might be some decisions that do not affect this utility node at all).
The value of each decision node will contain the expected global utility of each of the choices, indexed by previous decision nodes and informational predecessors.
What Choice to Make?
The first decision node will contain the expected utility of each of the choices. The one with the highest expected utility is the choice to make. Then, continue to the next decision node and look for the highest expected utility (conditioned in the previous decision node) and choose it. Continue to do the same until you run out of decision nodes.
