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

*Proceedings of Thirty Sixth Conference on Learning Theory*, PMLR 195:2211-2239, 2023.

#### Abstract

We study the problem of PAC learning $\gamma$-margin halfspaces with Random Classification Noise. We establish an information-computation tradeoffsuggesting 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 resultis 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.