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

TL;DR

This paper introduces Active Expansion Sampling (AES), a novel active learning method that efficiently identifies feasible domains in unbounded input spaces, overcoming limitations of fixed bounds in traditional methods.

Contribution

AES is the first method to adaptively expand input bounds during active learning, providing guarantees on misclassification loss within the explored region.

Findings

AES effectively identifies feasible domains in unbounded spaces.

AES outperforms fixed-bound methods like Neighborhood-Voronoi and straddle heuristic.

AES provides real-time feasibility prediction with theoretical guarantees.

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.