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Continuous Decision Variables with Multiple Continuous Parents

By Barry R. Cobb


This paper introduces an influence diagram (ID) model that permits continuous decision variables with multiple continuous parents. The marginalization operation for a continuous decision variable first develops a piecewise linear decision rule as a continuous function of the next continuous parent in the deletion sequence. Least squares regression is used to convert this rule to a piecewise linear function of all the decision variable’s continuous parents. This procedure is incorporated into an iterative solution algorithm that allows more refined decision rules to be constructed once the non-optimal regions of the state spaces of decision variables are identified. Additional examples serve to compare relative advantages of this technique to other ID models proposed in the literature.

Year: 2010
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