07/03/2025 at 13.00
Generating Point Sets of Small Star Discrepancy
Recording
Carola Doerr
13. 3. 2025 at 15:00, IJS main lecture hall (Jamova 39)
Recording
Generating Point Sets of Small Star Discrepancy
Carola Doerr, CNRS research director at Sorbonne Université, Paris, France
Carola Doerr, formerly Winzen, is a CNRS research director at Sorbonne Université in Paris, France. Carola's main research activities are in the analysis of black-box optimization algorithms, both by mathematical and by empirical means. She is particularly interested in dynamic choices of parameters and algorithms, and how to transfer experience from one optimization problem to another. Carola is associate editor of IEEE Transactions on Evolutionary Computation, ACM Transactions on Evolutionary Learning and Optimization (TELO), and Evolutionary Computation (ECJ). She participates in the organization of the main conferences in evolutionary computation and in Automated Machine Learning, in different roles. Carola's works have received several awards, among them the CNRS bronze medal, the Otto Hahn Medal of the Max Planck Society, best paper awards at GECCO, CEC, and EvoApplications. Her work is supported by an ERC Consolidator grant (dynaBBO, 2024-2029).

Uniformly distributed point sets of low discrepancy are heavily used in experimental design and across a very wide range of applications such as numerical integration, computer graphics, and finance. Recent methods based on Graph Neural Networks [Rusch et al., PNAS 2024] and solver-based optimization [Clément et al., accepted in Proceedings of the AMS] identified point sets having much lower discrepancy than previously known constructions. We show that further substantial improvements are possible by separating the construction of low-discrepancy point sets into (i) the relative position of the points, and (ii) the optimal placement respecting these relationships. Using tailored permutations, we construct point sets that are of 20\% smaller discrepancy on average than those proposed by Rusch et al. In terms of inverse discrepancy, our sets reduce the number of points in dimension 2 needed to obtain a discrepancy of 0.005 from more than 500 points to less than 350. For applications where the sets are used to query time-consuming models, this is a significant reduction.
The presentation is based on joint work with François Clément (University of Washington, US), Kathrin Klamroth (University of Wuppertal, Germany), and Luís Paquete (University of Coimbra, Portugal).

Zoom link:
https://zoom.us/j/91427615044?pwd=6hIVXIbu84vmbnFCUb0bnvRNAQyWlz.1

Carola Doerr
Carola Doerr, CNRS research director at Sorbonne Université, Paris, France