Limited Memory Influence Diagram¶
A limited memory influence diagram is a Bayesian network extended with decision facilities (decision nodes and utility nodes). The limited memory influence diagram (LIMID) extends the traditional influence diagram by relaxing two fundamental assumptions: a non-forgetting decision maker and a total order on decisions. In a LIMID all information available to the decision maker must be specified using informational links and decisions may by unordered.
Due to the elimination of the non-forgetting assumption of the decision maker it is in a LIMID important to specify for each decision exactly what information is available to the decision maker. Each variable which is observed prior to making a decision should have a link going into the decision. If the state of a node will be known at the time of making a decision, this will (probably) have an impact on what the decision maker should do. Thus, one must add a link from the node to the decision node.
If a node X is (informational) parent of a decision Di, but not parent of a subsequent decision Dj, this implies that X is known prior to decision Di, and not known at subsequent decision Dj,. This implies that the observation is not known by the decision maker at second decision.
The solution to a LIMID is a strategy consisting of one policy for each decision. The policy is a function from the known variables to the states of the decision. It is not a function of all past observations as the decision maker is assumed only to know the most recent observation on loses leaves. This is different from the traditional influence diagram where the policy would be a function from all past observations and decisions as the decision maker is assumed to be non-forgetting. There need not be a total order on the decisions.
Each decision in the LIMID has an initial policy which can be defined by the user either by hand or using expressions. The initial policy is a table specifying a mapping from configurations of the parents of the decision to states of the decision. This initial policy is updated in the process of solving the LIMID.
The solution to a LIMID is determined using Single Policy Updating.
An influence diagram cannot contain continuous chance nodes.