  In the arena of privacy-preserving machine learning, differentially private
stochastic gradient descent (DP-SGD) has outstripped the objective perturbation
mechanism in popularity and interest. Though unrivaled in versatility, DP-SGD
requires a non-trivial privacy overhead (for privately tuning the model's
hyperparameters) and a computational complexity which might be extravagant for
simple models such as linear and logistic regression. This paper revamps the
objective perturbation mechanism with tighter privacy analyses and new
computational tools that boost it to perform competitively with DP-SGD on
unconstrained convex generalized linear problems.
