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Optimal reconstruction from linear queries

Yuval Filmus, Shay Moran, and Elizaveta Nesterova
COLT 2026

We study the problem of locating an unknown point in $\mathbb{R}^d$ given linear queries $\langle u,x \rangle$ (where $u$ is a unit vector) which are answered with an additive error bounded by $\delta$. We show that the best error achievable given an unlimited number of queries is $\sqrt{\frac{2d}{d+1}} \delta$, and study the speed of convergence.

BibTeX

@inproceedings{FMN26,
title = {Optimal reconstruction from linear queries},
author = {Yuval Filmus and Shay Moran and Elizaveta Nesterova},
booktitle = {COLT 2026},
year = {2026}}
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