Which Directions Matter? Sparse Design for Affine Robust Optimization
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Computer Science > Machine Learning
Title:Which Directions Matter? Sparse Design for Affine Robust Optimization
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.
| Comments: | Accepted at UAI 2026 |
| Subjects: | Machine Learning (cs.LG); Optimization and Control (math.OC) |
| Cite as: | arXiv:2606.14648 [cs.LG] |
| (or arXiv:2606.14648v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.14648
arXiv-issued DOI via DataCite (pending registration)
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