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

• URL: http://arxiv.org/abs/2306.16352v1
• Date: Wed, 28 Jun 2023 16:33:39 GMT
• Title: Information-Computation Tradeoffs for Learning Margin Halfspaces with Random Classification Noise
• Authors: Ilias Diakonikolas, Jelena Diakonikolas, Daniel M. Kane, Puqian Wang, Nikos Zarifis
• Abstract summary: We study the problem of PAC $gamma$-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.
• Score: 50.64137465792738
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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