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Many engineering problems require identifying feasible domains under implicitconstraints. One example is finding acceptable car body styling designs basedon constraints like aesthetics and functionality. Current active-learning basedmethods learn feasible domains for bounded input spaces. However, we usuallylack prior knowledge about how to set those input variable bounds. Bounds thatare too small will fail to cover all feasible domains; while bounds that aretoo large will waste query budget. To avoid this problem, we introduce ActiveExpansion Sampling (AES), a method that identifies (possibly disconnected)feasible domains over an unbounded input space. AES progressively expands ourknowledge of the input space, and uses successive exploitation and explorationstages to switch between learning the decision boundary and searching for newfeasible domains. We show that AES has a misclassification loss guaranteewithin the explored region, independent of the number of iterations or labeledsamples. Thus it can be used for real-time prediction of samples' feasibilitywithin the explored region. We evaluate AES on three test examples and compareAES with two adaptive sampling methods -- the Neighborhood-Voronoi algorithmand the straddle heuristic -- that operate over fixed input variable bounds.

Active Expansion Sampling for Learning Feasible Domains in an Unbounded Input Space