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arXiv · 2501.09851

Learning Noisy Halfspaces with a Margin: Massart is No Harder than Random

Gautam Chandrasekaran·Vasilis Kontonis·Konstantinos Stavropoulos·Kevin Tian
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Abstract

We study the problem of PAC learning $\gamma$-margin halfspaces with Massart noise. We propose a simple proper learning algorithm, the Perspectron, that has sample complexity $\widetilde{O}((\epsilon\gamma)^{-2})$ and achieves classification error at most $\eta+\epsilon$ where $\eta$ is the Massart noise rate. Prior works [DGT19,CKMY20] came with worse sample complexity guarantees (in both $\epsilon$ and $\gamma$) or could only handle random classification noise [DDK+23,KIT+23] -- a much milder noise assumption. We also show that our results extend to the more challenging setting of learning generalized linear models with a known link function under Massart noise, achieving a similar sample complexity to the halfspace case. This significantly improves upon the prior state-of-the-art in this setting due to [CKMY20], who introduced this model.

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Gautam Chandrasekaran, Vasilis Kontonis, Konstantinos Stavropoulos, Kevin Tian. 2025-01-16. Learning Noisy Halfspaces with a Margin: Massart is No Harder than Random. https://arxiv.org/abs/2501.09851

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