DP-MAC: The Differentially Private Method of Auxiliary Coordinates for Deep Learning

TL;DR

DP-MAC introduces a novel differentially private deep learning method that uses auxiliary coordinates and Taylor expansion for efficient privacy-preserving training with improved convergence.

Contribution

It employs auxiliary coordinates and Taylor expansion to enable independent layer updates, improving convergence and privacy analysis over traditional gradient-based methods.

Findings

Achieves decent model quality under modest privacy budgets.

Faster convergence than stochastic gradient descent-based methods.

Provides tractable sensitivity analysis for deep neural networks.

Abstract

Developing a differentially private deep learning algorithm is challenging, due to the difficulty in analyzing the sensitivity of objective functions that are typically used to train deep neural networks. Many existing methods resort to the stochastic gradient descent algorithm and apply a pre-defined sensitivity to the gradients for privatizing weights. However, their slow convergence typically yields a high cumulative privacy loss. Here, we take a different route by employing the method of auxiliary coordinates, which allows us to independently update the weights per layer by optimizing a per-layer objective function. This objective function can be well approximated by a low-order Taylor's expansion, in which sensitivity analysis becomes tractable. We perturb the coefficients of the expansion for privacy, which we optimize using more advanced optimization routines than SGD for faster convergence. We empirically show that our algorithm provides a decent trained model quality under a modest privacy budget.