AI 中文总结
该研究在分布无关的基于样本模型中，证明半空间测试的样本复杂度下界为Θ(n/ε)，为单侧测试者给出匹配上界，明确双侧测试者无效率优势。
AI 中文摘要
我们针对在分布无关、基于样本的模型中，证明了测试实数域上半空间所需样本数的紧下界为Θ(n/ε)，该模型中底层概率分布对算法未知，算法仅能接收随机样本（无法发起查询）。这表明半空间测试的效率不高于其学习效率。我们还为单侧测试者证明了匹配的上界，改进了标准的（双侧）“通过学习进行测试”归约，确定该模型中的双侧半空间测试者相比单侧测试者无优势。
英文摘要
We prove a tight $Θ(n/ε)$ lower bound on the number of samples required for testing halfspaces over $\mathbb{R}^n$, in the distribution-free sample-based model where the underlying probability distribution is unknown to the algorithm, and the algorithm only receives random samples (i.e., it cannot make queries). This shows that testing is no more efficient than learning for halfspaces. We also show a matching upper bound for one-sided testers, improving on the standard (two-sided) testing-by-learning reduction, establishing that two-sided halfspace testers in this model have no advantage over one-sided testers.
