Decision Making with Interval Influence Diagrams

TL;DR

This paper extends influence diagrams to handle interval-valued probabilities and value functions, enabling robust decision analysis with bounds on expected outcomes considering input imprecision.

Contribution

It introduces procedures for decision making in influence diagrams with interval probabilities and value functions, including chance and decision node removal, with proven optimality and soundness.

Findings

The algorithm provides admissible decision alternatives and bounds on expected value.

Performance is comparable to exact algorithms on test influence diagrams.

The method offers an approximation to comprehensive sensitivity analysis.

Abstract

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.