Title: Generating Point Sets of Small Star Discrepancy

Speaker: Carola Doerr
National Centre for Scientific Research (CNRS), France

Abstract:
The $L_{\infty}$ star discrepancy is a very well-studied measure used to quantify the uniformity of a point set distribution. Constructing optimal point sets for this measure is seen as a very hard problem in the discrepancy community. Indeed, provably optimal point sets were known, up to now, only for up to 6 points in dimension 2 and up to two points in higher dimensions. 

In this talk, we will present different approaches to construct low discrepancy sets. We first introduce mathematical programming formulations to construct point sets with optimal $L_{\infty}$ star discrepancy values in dimension 2 for up to 21 points and 8 points in dimension 3. We show that these optimal sets have a far lower discrepancy than the previous references. More importantly, they present a very different structure. We will then discuss extensions of this approach to obtain good, but not provably optimal, point sets and show that there is much room for improvement over state-of-the-art constructions. We also show that additional symmetry requirements can be satisfied at very small loss in discrepancy value. Finally, we will discuss some recent advances using graph neural networks by Rusch et al. and how we outperform these constructions using classic optimisations approaches. 

Key references: Constructing optimal star discrepancy sets and Searching permutations for constructing uniformly distributed point sets

The presentation is based on joint work with François Clément (University of Washington, US), Kathrin Klamroth (Universoty of Wuppertal, Germany), and Luís Paquete (University of Coimbra, Portugal).

Biography:
Carola Doerr, formely Winzen, is a CNRS research director at Sorbonne Université in Paris, France, and scientific advisor for the CNRS informatics institute. Carola’s main research activities are in the analysis of black-box optimisation algorithms, both by mathematical and empirical means. She is also passionate about applications of iterative research algorithms in practice, be it in industrial or in academic contexts.

Carola is associate editor of IEEE Transactions Evolutionary Computation, ACM Transactions on Evolutionary Learning and Optimisation (TELO), and the Evolutionary Computation journal. She was program chair for AutoML 2025, the BBSR track at GECCO 2025 and 2024, the GECH track at GECCO 2023, for PPSN 2020, FOGA 2019, and for the theory tracks of GECCO 2015 and 2017. She has organised several Dagstuhl seminars and Lorentz Center workshops. Together with Pascal Kerschke, Carola leads the ‘Algorithm selection and configuration’ working group of COST action CA22137.

Carola’s works have been distinguished by several awards, among them the CNRS bronze medal, the Otto Hahn Medal for the Max Planck Society, and best paper awards at GECCO, CEC, and EvoApplications.

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WED 08 OCTOBER 2025 17:00 -18:00 (AEDT)/ 08:00 – 09:00 (CEST)