Order-of-Magnitude Influence Diagrams

Influence diagrams are a widely used framework for decision making under uncertainty. These models allow for a concise graphical representation of both probabilistic as well as utility information which in turn supports efficient graph-based algorithms for computing an optimal decision policy that maximizes the expected utility of the decision maker. In this paper we extend the framework to incorporate a qualitative rather than quantitative representation of the information based on order-of-magnitude probability and utility function. We also develop a variable elimination algorithm that generates an order-of-magnitude optimal policy. Furthermore, our model supports totally as well as partially ordered utilities. Numerical experiments on random influence diagrams analyze the quality of the order-of-magnitude policy with respect to the optimal policy derived from a corresponding regular influence diagram with exact probabilities and utility values.

By: Radu Marinescu; Nic Wilson

Published in: RC25100 in 2011


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