Which Directions Matter? Sparse Design for Affine Robust Optimization
Pedro Chumpitaz-Flores, My Duong, Juan S. Borrero, Kaixun Hua
Abstract
Robust machine learning and optimization rely on the uncertainty model choice. We investigate which uncertainty directions a model must cover when defined by a finite dictionary and a budget constraint. Selecting a subset forms an atomic uncertainty set with a closed form support function, yielding tractable robust programs for affine objectives. We propose a data driven selection rule based on a coverage objective over evaluation directions, including gradients, adversarial perturbations, or shifts observed on held out data. We prove this objective is monotone and submodular, supporting a greedy method with a $(1-1/e)$ approximation guarantee and a matching hardness barrier. We also provide a certificate bounding the loss from the selected subset and a radius calibration rule with out of sample control.
Topics
Classified with taxonomy v2 on Sat, 5 Sept 2026.