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arXiv · 2310.15411

Efficient Active Learning Halfspaces with Tsybakov Noise: A Non-convex Optimization Approach

Yinan Li·Chicheng Zhang
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Abstract

We study the problem of computationally and label efficient PAC active learning $d$-dimensional halfspaces with Tsybakov Noise~\citep{tsybakov2004optimal} under structured unlabeled data distributions. Inspired by~\cite{diakonikolas2020learning}, we prove that any approximate first-order stationary point of a smooth nonconvex loss function yields a halfspace with a low excess error guarantee. In light of the above structural result, we design a nonconvex optimization-based algorithm with a label complexity of $\tilde{O}(d (\frac{1}{\epsilon})^{\frac{8-6\alpha}{3\alpha-1}})$, under the assumption that the Tsybakov noise parameter $\alpha \in (\frac13, 1]$, which narrows down the gap between the label complexities of the previously known efficient passive or active algorithms~\citep{diakonikolas2020polynomial,zhang2021improved} and the information-theoretic lower bound in this setting.

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Yinan Li, Chicheng Zhang. 2023-10-23. Efficient Active Learning Halfspaces with Tsybakov Noise: A Non-convex Optimization Approach. https://arxiv.org/abs/2310.15411

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