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- W4288804597 abstract "We study the complexity of PAC learning halfspaces in the presence of Massart noise. In this problem, we are given i.i.d. labeled examples $(mathbf{x}, y) in mathbb{R}^N times { pm 1}$, where the distribution of $mathbf{x}$ is arbitrary and the label $y$ is a Massart corruption of $f(mathbf{x})$, for an unknown halfspace $f: mathbb{R}^N to { pm 1}$, with flipping probability $eta(mathbf{x}) leq eta < 1/2$. The goal of the learner is to compute a hypothesis with small 0-1 error. Our main result is the first computational hardness result for this learning problem. Specifically, assuming the (widely believed) subexponential-time hardness of the Learning with Errors (LWE) problem, we show that no polynomial-time Massart halfspace learner can achieve error better than $Omega(eta)$, even if the optimal 0-1 error is small, namely $mathrm{OPT} = 2^{-log^{c} (N)}$ for any universal constant $c in (0, 1)$. Prior work had provided qualitatively similar evidence of hardness in the Statistical Query model. Our computational hardness result essentially resolves the polynomial PAC learnability of Massart halfspaces, by showing that known efficient learning algorithms for the problem are nearly best possible." @default.
- W4288804597 created "2022-07-30" @default.
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- W4288804597 date "2022-07-28" @default.
- W4288804597 modified "2023-10-16" @default.
- W4288804597 title "Cryptographic Hardness of Learning Halfspaces with Massart Noise" @default.
- W4288804597 doi "https://doi.org/10.48550/arxiv.2207.14266" @default.
- W4288804597 hasPublicationYear "2022" @default.
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