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

Cite As Get 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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References

  1. Selin Damla Ahipaşaoğlu. A first-order algorithm for the A-optimal experimental design problem: a mathematical programming approach. Statistics and Computing, 25(6):1113-1127, 2015. Google Scholar
  2. Selin Damla Ahipaşaoğlu. A branch-and-bound algorithm for the exact optimal experimental design problem. Statistics and Computing, 31(5):65, 2021. Google Scholar
  3. Mathieu Besançon, Alejandro Carderera, and Sebastian Pokutta. FrankWolfe.jl: A high-performance and flexible toolbox for Frank-Wolfe algorithms and conditional gradients. INFORMS Journal on Computing, 2022. Google Scholar
  4. Ksenia Bestuzheva, Mathieu Besançon, Wei-Kun Chen, Antonia Chmiela, Tim Donkiewicz, Jasper van Doornmalen, Leon Eifler, Oliver Gaul, Gerald Gamrath, Ambros Gleixner, et al. Enabling research through the SCIP Optimization Suite 8.0. ACM Transactions on Mathematical Software, 49(2):1-21, 2023. Google Scholar
  5. Gábor Braun, Alejandro Carderera, Cyrille W Combettes, Hamed Hassani, Amin Karbasi, Aryan Mokhtari, and Sebastian Pokutta. Conditional gradient methods. arXiv preprint arXiv:2211.14103, 2022. Google Scholar
  6. Gábor Braun, Sebastian Pokutta, and Daniel Zink. Lazifying conditional gradient algorithms. In International conference on machine learning, pages 566-575. PMLR, 2017. Google Scholar
  7. Alejandro Carderera, Mathieu Besançon, and Sebastian Pokutta. Scalable Frank-Wolfe on generalized self-concordant functions via simple steps. SIAM Journal on Optimization, 2024. To appear. Google Scholar
  8. Chris Coey, Lea Kapelevich, and Juan Pablo Vielma. Conic optimization with spectral functions on Euclidean Jordan algebras. Mathematics of Operations Research, 2022. Google Scholar
  9. Chris Coey, Lea Kapelevich, and Juan Pablo Vielma. Performance enhancements for a generic conic interior point algorithm. Mathematical Programming Computation, 2022. URL: https://doi.org/10.1007/s12532-022-00226-0.
  10. Chris Coey, Lea Kapelevich, and Juan Pablo Vielma. Solving natural conic formulations with Hypatia.jl. INFORMS Journal on Computing, 34(5):2686-2699, 2022. URL: https://doi.org/10.1287/ijoc.2022.1202.
  11. Chris Coey, Miles Lubin, and Juan Pablo Vielma. Outer approximation with conic certificates for mixed-integer convex problems. Mathematical Programming Computation, 12(2):249-293, 2020. Google Scholar
  12. P Fernandes de Aguiar, B Bourguignon, MS Khots, DL Massart, and R Phan-Than-Luu. D-optimal designs. Chemometrics and intelligent laboratory systems, 30(2):199-210, 1995. Google Scholar
  13. Marguerite Frank and Philip Wolfe. An algorithm for quadratic programming. Naval research logistics quarterly, 3(1-2):95-110, 1956. Google Scholar
  14. Deborah Hendrych, Hannah Troppens, Mathieu Besançon, and Sebastian Pokutta. Convex mixed-integer optimization with Frank-Wolfe methods, 2023. URL: https://arxiv.org/abs/2208.11010.
  15. Qi Huangfu and Julian Hall. Parallelizing the dual revised simplex method. Mathematical Programming Computation, 10(1):119-142, 2018. Google Scholar
  16. Lea Kapelevich. How to optimize trace of matrix inverse with JuMP or Convex? https://discourse.julialang.org/t/how-to-optimize-trace-of-matrix-inverse-with-jump-or-convex/94167/6, accessed 4th December 2023, 2023.
  17. Jan Kronqvist, David E Bernal, Andreas Lundell, and Ignacio E Grossmann. A review and comparison of solvers for convex MINLP. Optimization and Engineering, 20:397-455, 2019. Google Scholar
  18. Evgeny S Levitin and Boris T Polyak. Constrained minimization methods. USSR Computational mathematics and mathematical physics, 6(5):1-50, 1966. Google Scholar
  19. Yongchun Li, Marcia Fampa, Jon Lee, Feng Qiu, Weijun Xie, and Rui Yao. D-optimal data fusion: Exact and approximation algorithms. INFORMS Journal on Computing, 36(1):97-120, 2024. Google Scholar
  20. Yurii Nesterov and Arkadii Nemirovskii. Interior-point polynomial algorithms in convex programming. SIAM, 1994. Google Scholar
  21. Aleksandar Nikolov, Mohit Singh, and Uthaipon Tantipongpipat. Proportional volume sampling and approximation algorithms for A-optimal design. Mathematics of Operations Research, 47(2):847-877, 2022. Google Scholar
  22. Gabriel Ponte, Marcia Fampa, and Jon Lee. Branch-and-bound for D-optimality with fast local search and variable-bound tightening. arXiv preprint arXiv:2302.07386, 2023. Google Scholar
  23. Friedrich Pukelsheim. Optimal design of experiments. SIAM, 2006. Google Scholar
  24. Guillaume Sagnol and Radoslav Harman. Computing exact D-optimal designs by mixed integer second-order cone programming. The Annals of Statistics, 43(5):2198-2224, 2015. URL: https://doi.org/10.1214/15-AOS1339.
  25. NV Sahinidis and Ignacio E Grossmann. Convergence properties of generalized Benders decomposition. Computers & Chemical Engineering, 15(7):481-491, 1991. Google Scholar
  26. Tianxiao Sun and Quoc Tran-Dinh. Generalized self-concordant functions: a recipe for Newton-type methods. Mathematical Programming, 178(1-2):145-213, 2019. Google Scholar
  27. William J Welch. Branch-and-bound search for experimental designs based on D optimality and other criteria. Technometrics, 24(1):41-48, 1982. Google Scholar
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