Title: Active Expansion Sampling for Learning Feasible Domains in an Unbounded Input Space,
Abstract: Many engineering problems require identifying feasible domains under implicit
constraints. One example is finding acceptable car body styling designs based
on constraints like aesthetics and functionality. Current active-learning based
methods learn feasible domains for bounded input spaces. However, we usually
lack prior knowledge about how to set those input variable bounds. Bounds that
are too small will fail to cover all feasible domains; while bounds that are
too large will waste query budget. To avoid this problem, we introduce Active
Expansion Sampling (AES), a method that identifies (possibly disconnected)
feasible domains over an unbounded input space. AES progressively expands our
knowledge of the input space, and uses successive exploitation and exploration
stages to switch between learning the decision boundary and searching for new
feasible domains. We show that AES has a misclassification loss guarantee
within the explored region, independent of the number of iterations or labeled
samples. Thus it can be used for real-time prediction of samples' feasibility
within the explored region. We evaluate AES on three test examples and compare
AES with two adaptive sampling methods -- the Neighborhood-Voronoi algorithm
and the straddle heuristic -- that operate over fixed input variable bounds.