Forschungsleitung (Direction de recherche) : Carola DOERR

Construction of Low-Discrepancy Point Sets via Optimization Approaches

Given a point set of size n, we want to find the subset of size m of minimal star discrepancy (a specific measure of discrepancy). Initial results obtained recently by C. Doerr and L. Paquete (Coimbra University) were promising and during this thesis we will aim to provide a more formal approach to the problem, as well as provide new algorithms and theoretical bounds, both for the exact problem as for approximations. Our approach will be both theoretical, via complexity analysis and algorithm development, and practical, with extensive testing of our algorithms and searching for the different applications of our new approach to discrepancy. We will be working with different branches of mathematics and computer science (Operations, Research, Algorithmic Theory, Discrepancy Theory) and it is highly likely that that the resolution of our problem will bring us to develop new tools or proofs in these different fields.

Verteidigung einer Doktorarbeit : 18.07.2024

Mitglieder der Prüfungskommission :

Jury:
-> Pr. Dmitriy Bilyk (reviewer), University of Minnesota, United States of America
-> Priv.-Doz. Mag. Dr. Peter Kritzer (reviewer), Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Austria
-> Dr. Claire Mathieu (examinator), CNRS, Université Paris Cité, IRIF, France
-> Pr. Art B. Owen (examinator), Stanford University, United States of America
-> Dr. Julien Tierny (examinator), CNRS, Sorbonne Université, LIP6, France
-> Dr Carola Doerr (PhD supervisor), CNRS, Sorbonne Université, LIP6, France
-> Dr Luís Paquete (PhD supervisor), DEI, University of Coimbra, Portugal

Publikationen 2022-2026

• 2026
  • C. Benjamins, H. Graf, S. Segel, D. Deng, T. Ruhkopf, L. Hennig, S. Basu, N. Mallik, E. Bergman, D. Chen, F. Clément, A. Tornede, M. Feurer, K. Eggensperger, F. Hutter, C. Doerr, M. Lindauer : “carps: A Framework for Comparing N Hyperparameter Optimizers on M Benchmarks”, Transactions on Machine Learning Research, ([Amherst Massachusetts]: OpenReview.net, 2022) (2026)
• 2025
  • F. Clément, C. Doerr, K. Klamroth, L. Paquete : “Constructing Optimal Star Discrepancy Sets”, Proceedings of the American Mathematical Society, Series B, vol. 12 (7), pp. 78-90 (2025)
  • F. Clément, C. Doerr, K. Klamroth, L. Paquete : “Searching permutations for constructing uniformly distributed point sets”, Proceedings of the National Academy of Sciences of the United States of America, vol. 122 (14), pp. e2424464122, (National Academy of Sciences) (2025)
• 2024
  • F. Clément : “La Construction d’Ensembles de Points à Faible Discrépance via des Approches d’Optimisation”, these, verteidigung einer doktorarbeit 18.07.2024, forschungsleitung (direction de recherche) Doerr, Carola (2024)
  • F. Clément, C. Doerr, L. Paquete : “Heuristic approaches to obtain low-discrepancy point sets via subset selection”, Journal of Complexity, vol. 83, pp. 101852, (Elsevier) (2024)
• 2023
  • F. Clément, D. Vermetten, J. De Nobel, A. Jesus, L. Paquete, C. Doerr : “Computing Star Discrepancies with Numerical Black-Box Optimization Algorithms”, GECCO '23: Genetic and Evolutionary Computation Conference, Lisbon, Portugal, pp. 1330-1338, (ACM) (2023)
• 2022
  • F. Clément, C. Doerr, L. Paquete : “Star Discrepancy Subset Selection: Problem Formulation and Efficient Approaches for Low Dimensions”, Journal of Complexity, vol. 70, pp. 101645, (Elsevier) (2022)