Near-Optimal Cryptographic Hardness of Learning With Homogeneous Halfspaces Under Gaussian Marginals
We study three problems that involve identifying homogeneous halfspaces under Gaussian distributions: agnostic learning, one-sided reliable learning, and fairness auditing. In each of these problems, we are given labeled examples $(\mathbf{x}, \mathrm{y})$ drawn from an unknown distribution on $\mathbb{R}^d\times\{-1, +1\}$, whose marginal distribution on $\mathbf{x}$ is standard Gaussian and on $\mathrm{y}$ is arbitrary. The goal of each problem is to output a homogeneous halfspace that approaches the best-fitting homogeneous halfspace in terms of its corresponding loss measure. We prove near-optimal computational hardness results for these problems under the widely believed hardness ass...
| Authors | Jizhou Huang, Brendan Juba |
|---|---|
| Primary category | cs.LG |
| Published | 29 April 2026 |
| Last updated at source | 29 April 2026 |
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