We study the differentially private (DP) empirical risk minimization (ERM) problem under the semi-sensitive DP setting where only some features are sensitive. This generalizes the Label DP setting where only the label is sensitive. We give improved upper and lower bounds on the excess risk for DP-ERM. In particular, we show that the error only scales polylogarithmically in terms of the sensitive domain size, improving upon previous results that scale polynomially in the sensitive domain size (Ghazi et al., 2021).

翻译：我们研究了在半敏感差分隐私（DP）设置下的差分隐私经验风险最小化（ERM）问题，其中仅部分特征为敏感特征。这推广了标签DP设置（即仅标签为敏感特征的情形）。我们针对DP-ERM的过量风险给出了改进的上界与下界。特别地，我们证明了误差仅随敏感域大小的多对数项缩放，改进了先前工作中误差随敏感域大小多项式缩放的结果（Ghazi等人，2021）。