Optimal Algorithms for Nonlinear Estimation with Convex Models
Abstract
A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other simple functionals of the object can be optimally estimated by functionals of the observations that share a similar simple structure. This is established for the maximum of several linear functionals and even for the th largest among them. Proving the latter requires an unusual refinement of the analytical Hahn--Banach theorem. The existence results are accompanied by practical recipes relying on convex optimization to construct the desired functionals, thereby justifying the term of estimation algorithms.
Cite
@article{arxiv.2512.20826,
title = {Optimal Algorithms for Nonlinear Estimation with Convex Models},
author = {Simon Foucart},
journal= {arXiv preprint arXiv:2512.20826},
year = {2025}
}