High-Dimensional Private Empirical Risk Minimization by Greedy Coordinate Descent
Abstract
In this paper, we study differentially private empirical risk minimization (DP-ERM). It has been shown that the worst-case utility of DP-ERM reduces polynomially as the dimension increases. This is a major obstacle to privately learning large machine learning models. In high dimension, it is common for some model's parameters to carry more information than others. To exploit this, we propose a differentially private greedy coordinate descent (DP-GCD) algorithm. At each iteration, DP-GCD privately performs a coordinate-wise gradient step along the gradients' (approximately) greatest entry. We show theoretically that DP-GCD can achieve a logarithmic dependence on the dimension for a wide range of problems by naturally exploiting their structural properties (such as quasi-sparse solutions). We illustrate this behavior numerically, both on synthetic and real datasets.
Cite
@article{arxiv.2207.01560,
title = {High-Dimensional Private Empirical Risk Minimization by Greedy Coordinate Descent},
author = {Paul Mangold and Aurélien Bellet and Joseph Salmon and Marc Tommasi},
journal= {arXiv preprint arXiv:2207.01560},
year = {2023}
}