Sound Abstraction of Probabilistic Actions in The Constraint Mass Assignment Framework

AnHai Doan , Peter Haddawy

Decision Systems and Artificial Intelligence Laboratory Department of EE & CS University of Wisconsin­Milwaukee Milwaukee, WI 53201

Abstract

This paper provides a formal and practical framework for sound abstraction of prob­ abilistic actions. We start by precisely defining the concept of sound abstraction within the context of finite­horizon plan­ ning (where each plan is a finite sequence of actions). Next we show that such abstrac­ tion cannot be performed within the tra­ ditional probabilistic action representation, which models a world with a single prob­ ability distribution over the state space. We then present the constraint mass as­ signment representation, which models the world with a set of probability distributions and is a generalization of mass assignment representations. Within this framework, we present sound abstraction procedures for three types of action abstraction. We end the paper with discussions and related work on sound and approximate abstraction. We give pointers to papers in which we discuss other sound abstraction­related issues, in­ cluding applications, estimating loss due to abstraction, and automatically generating abstraction hierarchies.