  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.
