Active Level Set Estimation for Continuous Search Space with Theoretical
  Guarantee
Giang Ngo Dang Nguyen Dat Phan-Trong Sunil Gupta
A common problem encountered in many real-world applications is level set
estimation where the goal is to determine the region in the function domain
where the function is above or below a given threshold. When the function is
black-box and expensive to evaluate, the level sets need to be found in a
minimum set of function evaluations. Existing methods often assume a discrete
search space with a finite set of data points for function evaluations and
estimating the level sets. When applied to a continuous search space, these
methods often need to first discretize the space which leads to poor results
while needing high computational time. While some methods cater for the
continuous setting, they still lack a proper guarantee for theoretical
convergence. To address this problem, we propose a novel algorithm that does
not need any discretization and can directly work in continuous search spaces.
Our method suggests points by constructing an acquisition function that is
defined as a measure of confidence of the function being higher or lower than
the given threshold. A theoretical analysis for the convergence of the
algorithm to an accurate solution is provided. On multiple synthetic and
real-world datasets, our algorithm successfully outperforms state-of-the-art
methods.