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arXiv · 2306.16352

Information-Computation Tradeoffs for Learning Margin Halfspaces with Random Classification Noise

Ilias Diakonikolas·Jelena Diakonikolas·Daniel M. Kane·Puqian Wang·Nikos Zarifis
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Abstract

We study the problem of PAC learning $\gamma$-margin halfspaces with Random Classification Noise. We establish an information-computation tradeoff suggesting an inherent gap between the sample complexity of the problem and the sample complexity of computationally efficient algorithms. Concretely, the sample complexity of the problem is $\widetilde{\Theta}(1/(\gamma^2 \epsilon))$. We start by giving a simple efficient algorithm with sample complexity $\widetilde{O}(1/(\gamma^2 \epsilon^2))$. Our main result is a lower bound for Statistical Query (SQ) algorithms and low-degree polynomial tests suggesting that the quadratic dependence on $1/\epsilon$ in the sample complexity is inherent for computationally efficient algorithms. Specifically, our results imply a lower bound of $\widetilde{\Omega}(1/(\gamma^{1/2} \epsilon^2))$ on the sample complexity of any efficient SQ learner or low-degree test.

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BibTeXRIS

Ilias Diakonikolas, Jelena Diakonikolas, Daniel M. Kane, Puqian Wang, Nikos Zarifis. 2023-06-28. Information-Computation Tradeoffs for Learning Margin Halfspaces with Random Classification Noise. https://arxiv.org/abs/2306.16352

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