ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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Theoretical Foundations for Abstraction-Based Probabilistic Planning

ion-Based Probabilistic Planning Vu Ha Peter Haddawy Department of EE & CS University of Wisconsin-Milwaukee fvu, [email protected] Abstract Modeling worlds and actions under uncertainty is one of the central problems in the framework of decision-theoretic planning. The representation must be general enough to capture real-world problems but at the same time it must provide a basis upon which theoretical results can be derived. The central notion in the framework we propose here is that of the affine-operator, which serves as a tool for constructing (convex) sets of probability distributions, and which can be considered as a generalization of belief functions and interval mass assignments. Uncertainty in the state of the worlds is modeled with sets of probability distributions, represented by affine-trees, while actions are defined as tree-manipulators. A small set of key properties of the affine-operator is presented, forming the basis for most existing operator-based definitio..