Robust Super-Level Set Estimation Using Gaussian Processes

  • Andrea Zanette
  • Junzi Zhang
  • Mykel J. KochenderferEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11052)


This paper focuses on the problem of determining as large a region as possible where a function exceeds a given threshold with high probability. We assume that we only have access to a noise-corrupted version of the function and that function evaluations are costly. To select the next query point, we propose maximizing the expected volume of the domain identified as above the threshold as predicted by a Gaussian process, robustified by a variance term. We also give asymptotic guarantees on the exploration effect of the algorithm, regardless of the prior misspecification. We show by various numerical examples that our approach also outperforms existing techniques in the literature in practice.


Active learning Gaussian processes Level set estimation 



Blake Wulfe provided the simulator for the simulations experiments. The authors are grateful to the reviewers for their comments.

Supplementary material

478890_1_En_17_MOESM1_ESM.pdf (829 kb)
Supplementary material 1 (pdf 829 KB)


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Andrea Zanette
    • 1
  • Junzi Zhang
    • 1
  • Mykel J. Kochenderfer
    • 1
    Email author
  1. 1.Stanford UniversityStanfordUSA

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