Robustly Learning a Single Neuron via Sharpness

Puqian Wang, Nikos Zarifis, Ilias Diakonikolas, Jelena Diakonikolas
6/13/2023
cs.LGcs.DSmath.OC

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Abstract

We study the problem of learning a single neuron with respect to the $L_2^2$-loss in the presence of adversarial label noise. We give an efficient algorithm that, for a broad family of activations including ReLUs, approximates the optimal $L_2^2$-error within a constant factor. Our algorithm applies under much milder distributional assumptions compared to prior work. The key ingredient enabling our results is a novel connection to local error bounds from optimization theory.

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Cite this paper

@article{wang2023robustly,
  title  = {Robustly Learning a Single Neuron via Sharpness},
  author = {Puqian Wang and Nikos Zarifis and Ilias Diakonikolas and Jelena Diakonikolas},
  year   = {2023},
  eprint = {2306.07892},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2306.07892v1},
  journal = {ICML 2023 2023}
}

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