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# An Adaptive Strategy for Active Learning with Smooth Decision Boundary

## Author(s): Locatelli, Andrea; Carpentier, Alexandra; Kpotufe, Samory

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 Abstract: We present the first adaptive strategy for active learning in the setting of classification with smooth decision boundary. The problem of adaptivity (to unknown distributional parameters) has remained opened since the seminal work of Castro and Nowak (2007), which first established (active learning) rates for this setting. While some recent advances on this problem establish \emph{adaptive} rates in the case of univariate data, adaptivity in the more practical setting of multivariate data has so far remained elusive. Combining insights from various recent works, we show that, for the multivariate case, a careful reduction to univariate-adaptive strategies yield near-optimal rates without prior knowledge of distributional parameters. Publication Date: 2018 Citation: Locatelli, Andrea, Alexandra Carpentier, and Samory Kpotufe. "An Adaptive Strategy for Active Learning with Smooth Decision Boundary." In Proceedings of Algorithmic Learning Theory, PMLR 83, pp. 547-571. 2018. ISSN: 2640-3498 Pages: 547 - 571 Type of Material: Conference Article Journal/Proceeding Title: Proceedings of Algorithmic Learning Theory, PMLR Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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