Robust Super-Level Set Estimation Using Gaussian Processes

Abstract

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.

Bayesian Experimental Design for Finding Reliable Level Set Under Input Uncertainty

“…x , thus it is inappropriate to assume GP as in previous studies. Furthermore, acquisition functions such as Straddle [1], LSE [2] and MILE [3] proposed in previous studies cannot be used directly in our setting. In the following subsections, we propose a modeling method for p *…”

“…Then, [2] proposed a new AF based on GP-UCB [7] framework, and prove the convergence of the algorithm. Recently, [3] proposed another new AF for LSE problem based on expected improvement of classification accuracy. LSE problems are also used in the context of safe BO [8], [9].…”

“…In this subsection, we propose an acquisition function to determine a next evaluation point. Our proposed AF is based on the Maximum Improvement for Level-set Estimation (MILE) introduced by [3]. In MILE, the point that maximizes the expected classification improvement after adding one point is taken as the next evaluation point.…”

“…LSE is defined as the problem of identifying the input region in which the outputs of a function are smaller/greater than a certain threshold. In the statistics and machine learning literature, many methods for the LSE problem have been proposed [1]- [3].…”

Level Set Estimation with Search Space Warping

“…For super-level set estimation, [16] proposes Maximum Improvement for Level-Set Estimation (MILE), a one-step lookahead algorithm, to locate points that exceed a threshold with a specified high probability. Aiming to find the largest region that exists above a certain level, it operates by sampling points which provide the greatest expected improvement in the set of points classified as being above the threshold.…”