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In this paper, we consider the problem of actively learning a linearclassifier through query synthesis where the learner can construct artificialqueries in order to estimate the true decision boundaries. This problem hasrecently gained a lot of interest in automated science and adversarial reverseengineering for which only heuristic algorithms are known. In suchapplications, queries can be constructed de novo to elicit information (e.g.,automated science) or to evade detection with minimal cost (e.g., adversarialreverse engineering). We develop a general framework, called dimension coupling(DC), that 1) reduces a d-dimensional learning problem to d-1 low dimensionalsub-problems, 2) solves each sub-problem efficiently, 3) appropriatelyaggregates the results and outputs a linear classifier, and 4) provides atheoretical guarantee for all possible schemes of aggregation. The proposedmethod is proved resilient to noise. We show that the DC framework avoids thecurse of dimensionality: its computational complexity scales linearly with thedimension. Moreover, we show that the query complexity of DC is near optimal(within a constant factor of the optimum algorithm). To further support ourtheoretical analysis, we compare the performance of DC with the existing work.We observe that DC consistently outperforms the prior arts in terms of querycomplexity while often running orders of magnitude faster.

Near-Optimal Active Learning of Halfspaces via Query Synthesis in the Noisy Setting