English

The sample complexity of level set approximation

Statistics Theory 2021-02-24 v2 Machine Learning Statistics Theory

Abstract

We study the problem of approximating the level set of an unknown function by sequentially querying its values. We introduce a family of algorithms called Bisect and Approximate through which we reduce the level set approximation problem to a local function approximation problem. We then show how this approach leads to rate-optimal sample complexity guarantees for H{\"o}lder functions, and we investigate how such rates improve when additional smoothness or other structural assumptions hold true.

Keywords

Cite

@article{arxiv.2010.13405,
  title  = {The sample complexity of level set approximation},
  author = {François Bachoc and Tommaso Cesari and Sébastien Gerchinovitz},
  journal= {arXiv preprint arXiv:2010.13405},
  year   = {2021}
}
R2 v1 2026-06-23T19:38:40.964Z