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- W4320854906 abstract "We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples $(mathbf{x},y)$ from an unknown distribution on $mathbb{R}^n times { pm 1}$, whose marginal distribution on $mathbf{x}$ is the standard Gaussian and the labels $y$ can be arbitrary, the goal is to output a hypothesis with 0-1 loss $mathrm{OPT}+epsilon$, where $mathrm{OPT}$ is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression." @default.
- W4320854906 created "2023-02-16" @default.
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- W4320854906 date "2023-02-13" @default.
- W4320854906 modified "2023-09-29" @default.
- W4320854906 title "Near-Optimal Cryptographic Hardness of Agnostically Learning Halfspaces and ReLU Regression under Gaussian Marginals" @default.
- W4320854906 doi "https://doi.org/10.48550/arxiv.2302.06512" @default.
- W4320854906 hasPublicationYear "2023" @default.
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