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The sample complexity of level set approximation

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 Hölder functions, and we investigate how such rates improve when additional smoothness or other structural assumptions hold true.
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Contributor : François Bachoc <>
Submitted on : Friday, October 23, 2020 - 10:54:19 AM
Last modification on : Wednesday, January 20, 2021 - 3:38:29 AM


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  • HAL Id : hal-02976018, version 1
  • ARXIV : 2010.13405


François Bachoc, Tommaso Cesari, Sébastien Gerchinovitz. The sample complexity of level set approximation. 2020. ⟨hal-02976018⟩



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