Efficiently Learning Drifting Halfspaces with Massart Noise

Abstract:We study the problem of learning a drifting concept in the presence of Massart noise. In this framework, an online learner has access to a history of independent samples whose labels are noisy versions of a target concept that may change from round to round. The goal is to output, in each round, a hypothesis with small prediction error. We study the complexity of this learning problem for the fundamental class of margin-separable linear classifiers (halfspaces). On the positive side, we give a computationally efficient learner achieving error $\eta + \tilde O(\Delta^{1/3}/\gamma)$, where $\eta$ upper bounds the Massart noise rate, $\Delta$ is the drift rate, and $\gamma$ is the margin. Interestingly, in the realizable setting, an adaptation of our techniques yields an efficient learner with an improved error rate over prior work. On the lower-bound side, we provide formal evidence of an information-computation tradeoff, strongly suggesting that our algorithm's performance is essentially optimal. Specifically, while the information-theoretically optimal error scales with $\Delta^{1/2}$, we prove that $\Delta^{1/3}$-scaling is unavoidable for low-degree polynomial tests, even in the special case of random classification noise.

Machine Learning (cs.LG)

arXiv:2606.11149 [cs.LG]

(or arXiv:2606.11149v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2606.11149 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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