An Algebraic Graphical Model for Decision with Uncertainties, Feasibilities, and Utilities

Numerous formalisms and dedicated algorithms have been designed in the last decades to model and solve decision making problems. Some formalisms, such as constraint networks, can express “simple” decision problems, while others are designed to take into account uncertainties, unfeasible decisions, and utilities. Even in a single formalism, several variants are often proposed to model different types of uncertainty (probability, possibility...) or utility (additive or not). In this article, we introduce an algebraic graphical model that encompasses a large number of such formalisms: (1) we first adapt previous structures from Friedman, Chu and Halpern for representing uncertainty, utility, and expected utility in order to deal with generic forms of sequential decision making; (2) on these structures, we then introduce composite graphical models that express information via variables linked by “local” functions, thanks to conditional independence; (3) on these graphical models...

• Type: Journal
• Year: 2007
• Where: JAIR
• Authors: Cédric Pralet, Gérard Verfaillie, Thomas Schiex
• Keywords: Algebraic Graphical Model, Graphical Models, JAIR 2007, Numerous Formalisms