Active expansion sampling for learning feasible domains in an unbounded input space

Wei Chen*, Mark Fuge

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)925-945
Number of pages21
JournalStructural and Multidisciplinary Optimization
Issue number3
StatePublished - Mar 1 2018


  • Active learning
  • Adaptive sampling
  • Exploitation-exploration trade-off
  • Feasible domain identification
  • Gaussian process

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization

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