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Article Dans Une Revue INFORMS Journal on Optimization Année : 2020

Integer Programming on the Junction Tree Polytope for Influence Diagrams

Résumé

Influence diagrams (ID) and limited memory influence diagrams (LIMID) are flexible tools to represent discrete stochastic optimization problems, with the Markov decision process (MDP) and partially observable MDP as standard examples. More precisely, given random variables considered as vertices of an acyclic digraph, a probabilistic graphical model defines a joint distribution via the conditional distributions of vertices given their parents. In an ID, the random variables are represented by a probabilistic graphical model whose vertices are partitioned into three types: chance, decision, and utility vertices. The user chooses the distribution of the decision vertices conditionally to their parents in order to maximize the expected utility. Leveraging the notion of rooted junction tree, we present a mixed integer linear formulation for solving an ID, as well as valid inequalities, which lead to a computationally efficient algorithm. We also show that the linear relaxation yields an optimal integer solution for instances that can be solved by the “single policy update,” the default algorithm for addressing IDs.

Dates et versions

hal-03573225 , version 1 (14-02-2022)

Identifiants

Citer

Axel Parmentier, Victor Cohen, Vincent Leclère, Guillaume Obozinski, Joseph Salmon. Integer Programming on the Junction Tree Polytope for Influence Diagrams. INFORMS Journal on Optimization, 2020, 2 (3), pp.209-228. ⟨10.1287/ijoo.2019.0036⟩. ⟨hal-03573225⟩
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