On the Power of Localized Perceptron for Label-Optimal Learning of Halfspaces with Adversarial Noise

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Abstract

We study online active learning of homogeneous halfspaces in Rd with adversarial noise where the overall probability of a noisy label is constrained to be at most ν. Our main contribution is a Perceptron-like online active learning algorithm that runs in polynomial time, and under the conditions that the marginal distribution is isotropic log-concave and ν = Ω(ε), where ε∈ (0, 1) is the target error rate, our algorithm PAC learns the underlying halfspace with near-optimal label complexity of Õ(d·polylog(1 ε )) and sample complexity of Õ( d ε).1 Prior to this work, existing online algorithms designed for tolerating the adversarial noise are subject to either label complexity polynomial in 1 ε, or suboptimal noise tolerance, or restrictive marginal distributions. With the additional prior knowledge that the underlying halfspace is s-sparse, we obtain attribute-efficient label complexity of Õ(s · polylog(d, 1 ε )) and sample complexity of Õ(s ε · polylog(d)). As an immediate corollary, we show that under the agnostic model where no assumption is made on the noise rate ν, our active learner achieves an error rate of O(OPT) + ε with the same running time and label and sample complexity, where OPT is the best possible error rate achievable by any homogeneous halfspace.

Original languageEnglish
Title of host publicationProceedings of the 38th International Conference on Machine Learning, ICML 2021
Pages9503-9514
Number of pages12
ISBN (Electronic)9781713845065
StatePublished - 2021
Event38th International Conference on Machine Learning, ICML 2021 - Virtual, Online
Duration: 18 Jul 202124 Jul 2021

Publication series

NameProceedings of Machine Learning Research
Volume139
ISSN (Electronic)2640-3498

Conference

Conference38th International Conference on Machine Learning, ICML 2021
CityVirtual, Online
Period18/07/2124/07/21

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