We revisit the problem of differentially private squared error linear regression. We observe that existing state-of-the-art methods are sensitive to the choice of hyperparameters -- including the ``clipping threshold'' that cannot be set optimally in a data-independent way. We give a new algorithm for private linear regression based on gradient boosting. We show that our method consistently improves over the previous state of the art when the clipping threshold is taken to be fixed without knowledge of the data, rather than optimized in a non-private way -- and that even when we optimize the hyperparameters of competitor algorithms non-privately, our algorithm is no worse and often better. In addition to a comprehensive set of experiments, we give theoretical insights to explain this behavior.

翻译：我们重新审视了差分隐私平方误差线性回归问题。观察到现有最优方法对超参数选择敏感——包括无法以数据无关方式最优设定的“裁剪阈值”。我们提出了一种基于梯度提升的隐私线性回归新算法。研究表明，当裁剪阈值在未知数据的情况下固定设定（而非通过非隐私方式优化）时，我们的方法持续优于此前最优方法；即便以非隐私方式优化竞争算法的超参数，我们的算法性能也不逊于甚至优于它们。除全面的实验验证外，我们还从理论角度解释了这一现象。