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Using Neural Networks to Solve Linear Bilevel Problems with Unknown Lower Level

Submission Status:under review
  • Bilevel problems are used to model the interaction between two decision makers in which the lower-level problem, the so-called follower's problem, appears as a constraint in the upper-level problem of the so-called leader. One issue in many practical situations is that the follower's problem is not explicitly known by the leader. For such bilevel problems with unknown lower-level model we propose the use of neural networks to learn the follower's optimal response for given decisions of the leader based on available historical data of pairs of leader and follower decisions. Integrating the resulting neural network in a single-level reformulation of the bilevel problem leads to a challenging model with a black-box constraint. We exploit Lipschitz optimization techniques from the literature to solve this reformulation and illustrate the applicability of the proposed method with some preliminary case studies using academic and linear bilevel instances.
Metadaten
Author:Ioana Molan, Martin Schmidt
Document Type:Preprint
Language:English
Date of Publication (online):2022/07/01
Release Date:2022/07/04
Tag:Bilevel optimization; Lipschitz optimization; Neural networks; Unknown follower problems
Page Number:16
Institutes:Universität Trier
Subprojects:A05
B08
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International