Order-of-Magnitude Influence Diagrams

TL;DR

This paper introduces a qualitative framework for influence diagrams using order-of-magnitude approximations to model sequential decision making with imprecise information, along with a specialized variable elimination algorithm.

Contribution

It presents a novel qualitative approach to influence diagrams based on order-of-magnitude approximations and a new variable elimination algorithm for solving such diagrams.

Findings

Developed a qualitative theory for influence diagrams with imprecise data

Proposed an order-of-magnitude approximation method for probabilities and utilities

Designed a dedicated variable elimination algorithm for the new framework

Abstract

In this paper, we develop a qualitative theory of influence diagrams that can be used to model and solve sequential decision making tasks when only qualitative (or imprecise) information is available. Our approach is based on an order-of-magnitude approximation of both probabilities and utilities and allows for specifying partially ordered preferences via sets of utility values. We also propose a dedicated variable elimination algorithm that can be applied for solving order-of-magnitude influence diagrams.