Theoretical foundations for abstraction-based probabilistic planning

  • Authors:

  • Vu Ha;Peter Haddawy

  • Affiliations:

  • Department of EE & CS, University of Wisconsin-Milwaukee;Department of EE & CS, University of Wisconsin-Milwaukee

  • Venue:
  • UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
  • Year:
  • 1996

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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 definitions of probabilistie action projection and action abstraction. We derive and prove correct three projection rules, which vividly illustrate the precision-complexity tradeoff in plan projection. Finally, we show how the three types of action abstraction identified by Haddawy and Doan are manifested in the present framework.