Intrinsic perturbation scale for certified oracle objectives with epigraphic information
Optimization and Control
2026-04-08 v1 Machine Learning
Functional Analysis
Abstract
We introduce a natural displacement control for minimizer sets of oracle objectives equipped with certified epigraphic information. Formally, we replace the usual local uniform value control of objective perturbations - uncertifiable from finite pointwise information without additional structure - by the strictly weaker requirement of a cylinder-localized vertical epigraphic control, naturally provided by certified envelopes. Under set-based quadratic growth (allowing nonunique minimizers), this yields the classical square-root displacement estimate with optimal exponent 1/2, without any extrinsic assumption.
Keywords
Cite
@article{arxiv.2604.05678,
title = {Intrinsic perturbation scale for certified oracle objectives with epigraphic information},
author = {Karim Bounja and Boujemaâ Achchab and Abdeljalil Sakat},
journal= {arXiv preprint arXiv:2604.05678},
year = {2026}
}