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Paper No. 10-15

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RG Cowell, P Thwaites and JQ Smith

Decision making with decision event graphs

Abstract: We introduce a new modelling representation, the Decision Event Graph (DEG), for asymmetric multistage decision problems. The DEG explicitly encodes conditional independences and has additional significant advantages over other representations of asymmetric decision problems. The colouring of edges makes it possible to identify conditional independences on decision trees, and these coloured trees serve as a basis for the construction of the DEG. We provide an efficient backward-induction algorithm for finding optimal decision rules on DEGs, and work through an example showing the efficacy of these graphs. Simplifications of the topology of a DEG admit analogues to the sufficiency principle and barren node deletion steps used with influence diagrams.

Keywords: Asymmetric decision problem; Backwards induction; Decision tree; Extensive form; Influence diagram; Local computation; Optimal policy.