Decision Making with Interval Influence Diagrams
This work addresses decision-making under uncertainty with imprecise probabilities for AI and decision analysis, but it is incremental as it builds on prior interval probability frameworks.
The paper extends interval-based probabilistic reasoning in influence diagrams to include decision nodes and interval-valued value functions, deriving optimal and sound procedures for chance and decision node removal, and shows the algorithm's performance compared to an exact method.
In previous work (Fertig and Breese, 1989; Fertig and Breese, 1990) we defined a mechanism for performing probabilistic reasoning in influence diagrams using interval rather than point-valued probabilities. In this paper we extend these procedures to incorporate decision nodes and interval-valued value functions in the diagram. We derive the procedures for chance node removal (calculating expected value) and decision node removal (optimization) in influence diagrams where lower bounds on probabilities are stored at each chance node and interval bounds are stored on the value function associated with the diagram's value node. The output of the algorithm are a set of admissible alternatives for each decision variable and a set of bounds on expected value based on the imprecision in the input. The procedure can be viewed as an approximation to a full e-dimensional sensitivity analysis where n are the number of imprecise probability distributions in the input. We show the transformations are optimal and sound. The performance of the algorithm on an influence diagrams is investigated and compared to an exact algorithm.