Polytope Division Method: A Scalable Sampling Method for Problems with High-Dimensional Parameters
Year: 2025
Type: article
Abstract: . Configuration Optimization Problems (COPs), which involve minimizing a loss function over a set of discrete points [Formula: see text], are common in areas like Model Order Reduction, Active Learning, and Optimal Experimental Design. While exact solutions are often infeasible, heuristic methods such as the weak Greedy Sampling Method (wGSM) provide practical alternatives, particularly for low-dimensional cases. wGSM recursively updates [Formula: see text] by solving a continuous optimization problem, which is typically approximated by a search over a discrete sample set [Formula: see text]. However, as the dimensionality grows, the sample size suffers from the curse of dimensionality. To address this, we introduce the Polytope Division Method (PDM), a scalable greedy-type approach that adaptively partitions the parameter space and targets regions of high loss. PDM achieves linear scaling with problem dimensionality and offers an efficient solution approach for high-dimensional COPs, overcoming the limitations of traditional methods.
DOI: 10.1137/24m1704506
Authors: Evie Nielen, Oliver Tse, Karen Veroy
Institution: Eindhoven University of Technology
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
Awards: G2492938540, G434337789
OpenAlex ID: W4415985914