Decision with Uncertainties, Feasibilities, and Utilities: Towards a Unified Algebraic Framework

Several formalisms exist to express and solve decision problems. Each is designed to capture different kinds of knowledge: utilities expressing preferences, uncertainties on the environment, or feasibility constraints on the decisions, with a possible sequential aspect. Despite the fact that every framework relies on specific properties exploited by dedicated algorithms, these formalisms present interesting similarities. In this paper, we show that it is possible to capture these similarities in a generic algebraic framework for sequential decision making with uncertainties, feasibilities, and utilities. This framework subsumes several existing approaches, from constraint satisfaction problems to quantified boolean formulas, Bayesian networks or possibilistic Markov decision processes. We introduce this framework using a toy example, increasingly sophisticated by uncertainties, feasibilities and possible observations. This leads to a formal definition of the framework together with ded...

• Type: Conference
• Year: 2006
• Where: ECAI
• Authors: Cédric Pralet, Gérard Verfaillie, Thomas Schiex
• Keywords: Artificial Intelligence, Decision Problems, ECAI 2006, Generic Algebraic Framework, Possible Sequential Aspect