  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).
