High-Dimensional Private Empirical Risk Minimization by Greedy Coordinate Descent

Authors: Paul Mangold, Aurélien Bellet, Joseph Salmon, Marc Tommasi
Published: 2022-07-04 | Updated: 2023-04-09

Source: https://arxiv.org/abs/2207.01560

PDF: https://arxiv.org/pdf/2207.01560

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収束保証 アルゴリズム設計 最適化アルゴリズムの選択と評価

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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.