Complexity results and algorithms for possibilistic influence diagrams

Laurent Garcia (1) , Régis Sabbadin (2)

1 UA - Université d'Angers
2 UBIA - Unité de Biométrie et Intelligence Artificielle (ancêtre de MIAT)

In this article we present the framework of Possibilistic Influence Diagrams (PID), which allows to model in a compact form problems of sequential decision making under uncertainty, when only ordinal data on transitions likelihood or preferences are available. The graphical part of a PID is exactly the same as that of usual influence diagrams, however the semantics differ. Transition likelihoods are expressed as possibility distributions and rewards are here considered as satisfaction degrees. Expected utility is then replaced by anyone of the two possibilistic qualitative utility criteria (optimistic and pessimistic) for evaluating strategies in a PID.We then describe decision tree-based methods for evaluating PID and computing optimal strategies and we study the computational complexity of PID optimisation problems for both cases. Finally, we propose a dedicated variable elimination algorithm that can be applied to both optimistic and pessimistic cases for solving PID.

Mots clés: DECISION THEORY; POSSIBILITY THEORY; CAUSAL NETWORKS; INFLUENCE DIAGRAMS; PID

Mots clés: POSSIBILISTIC INFLUENCE DIAGRAMS; INTELLIGENCE ARTIFICIELLE

Domaines: Mathématiques [math]; Informatique [cs]

Laurent Garcia, Régis Sabbadin. Complexity results and algorithms for possibilistic influence diagrams. Artificial Intelligence, 2008, 172 (8-9), pp.1018-1044. ⟨10.1016/j.artint.2007.11.008⟩. ⟨hal-02661247⟩