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Active Learning of Classifiers with Label and Seed Queries

8 September 2022
Marco Bressan
Nicolò Cesa-Bianchi
Silvio Lattanzi
Andrea Paudice
Maximilian Thiessen
    VLM
ArXiv (abs)PDFHTML
Abstract

We study exact active learning of binary and multiclass classifiers with margin. Given an nnn-point set X⊂RmX \subset \mathbb{R}^mX⊂Rm, we want to learn any unknown classifier on XXX whose classes have finite strong convex hull margin, a new notion extending the SVM margin. In the standard active learning setting, where only label queries are allowed, learning a classifier with strong convex hull margin γ\gammaγ requires in the worst case Ω(1+1γ)(m−1)/2\Omega\big(1+\frac{1}{\gamma}\big)^{(m-1)/2}Ω(1+γ1​)(m−1)/2 queries. On the other hand, using the more powerful seed queries (a variant of equivalence queries), the target classifier could be learned in O(mlog⁡n)O(m \log n)O(mlogn) queries via Littlestone's Halving algorithm; however, Halving is computationally inefficient. In this work we show that, by carefully combining the two types of queries, a binary classifier can be learned in time poly⁡(n+m)\operatorname{poly}(n+m)poly(n+m) using only O(m2log⁡n)O(m^2 \log n)O(m2logn) label queries and O(mlog⁡mγ)O\big(m \log \frac{m}{\gamma}\big)O(mlogγm​) seed queries; the result extends to kkk-class classifiers at the price of a k!k2k!k^2k!k2 multiplicative overhead. Similar results hold when the input points have bounded bit complexity, or when only one class has strong convex hull margin against the rest. We complement the upper bounds by showing that in the worst case any algorithm needs Ω(kmlog⁡1γ)\Omega\big(k m \log \frac{1}{\gamma}\big)Ω(kmlogγ1​) seed and label queries to learn a kkk-class classifier with strong convex hull margin γ\gammaγ.

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