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Pré-publication, Document de travail

Mathematical programming for influence diagrams

Abstract : Influence Diagrams (ID) are a flexible tool to represent discrete stochastic optimization problems, including 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 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.
Type de document :
Pré-publication, Document de travail
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https://hal-enpc.archives-ouvertes.fr/hal-02043198
Contributeur : Vincent Leclère <>
Soumis le : mercredi 20 février 2019 - 17:55:08
Dernière modification le : lundi 4 mai 2020 - 11:04:07

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Identifiants

  • HAL Id : hal-02043198, version 1
  • ARXIV : 1902.07039

Citation

Axel Parmentier, Victor Cohen, Vincent Leclère, Guillaume Obozinski, Joseph Salmon. Mathematical programming for influence diagrams. 2019. ⟨hal-02043198⟩

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