Robust Super-Level Set Estimation using Gaussian Processes
This addresses the problem of efficient exploration in costly function evaluation for applications like environmental monitoring or engineering design, though it is incremental over existing Gaussian process methods.
The paper tackles the problem of identifying large regions where an expensive, noisy function exceeds a threshold by proposing a Gaussian process-based method that maximizes expected volume with variance robustness. The approach provides asymptotic guarantees against prior misspecification and outperforms existing techniques in numerical examples.
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.