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Solving the Optimal Experiment Design Problem with Mixed-Integer Convex Methods

Authors Deborah Hendrych , Mathieu Besançon , Sebastian Pokutta

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Author Details

Deborah Hendrych
  • Zuse Institute Berlin, Germany
  • Technische Universität Berlin, Germany
Mathieu Besançon
  • Université Grenoble Alpes, Inria, LIG, Grenoble, France
  • Zuse Institute Berlin, Germany
Sebastian Pokutta
  • Technische Universität Berlin, Germany
  • Zuse Institute Berlin, Germany

Funding

Research reported in this paper was partially supported through the Research Campus Modal funded by the German Federal Ministry of Education and Research (fund numbers 05M14ZAM,05M20ZBM) and the Deutsche Forschungsgemeinschaft (DFG) through the DFG Cluster of Excellence MATH+.

Cite AsGet BibTex

Deborah Hendrych, Mathieu Besançon, and Sebastian Pokutta. Solving the Optimal Experiment Design Problem with Mixed-Integer Convex Methods. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 16:1-16:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SEA.2024.16

Abstract

We tackle the Optimal Experiment Design Problem, which consists of choosing experiments to run or observations to select from a finite set to estimate the parameters of a system. The objective is to maximize some measure of information gained about the system from the observations, leading to a convex integer optimization problem. We leverage Boscia.jl, a recent algorithmic framework, which is based on a nonlinear branch-and-bound algorithm with node relaxations solved to approximate optimality using Frank-Wolfe algorithms. One particular advantage of the method is its efficient utilization of the polytope formed by the original constraints which is preserved by the method, unlike alternative methods relying on epigraph-based formulations. We assess our method against both generic and specialized convex mixed-integer approaches. Computational results highlight the performance of our proposed method, especially on large and challenging instances.

Subject Classification

ACM Subject Classification
  • Theory of computation → Branch-and-bound
  • Theory of computation → Integer programming
  • Theory of computation → Convex optimization
Keywords
  • Mixed-Integer Non-Linear Optimization
  • Optimal Experiment Design
  • Frank-Wolfe
  • Boscia

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