Stability Enhanced Privacy and Applications in Private Stochastic Gradient Descent

TL;DR

This paper explores how algorithmic stability can enhance privacy in private stochastic gradient descent, providing theoretical bounds and experimental validation for improved privacy-utility tradeoffs in machine learning.

Contribution

It establishes a theoretical link between stability and differential privacy in strongly-convex loss functions, unifying and extending privacy guarantees for stabilized SGD methods.

Findings

Stability implies a bound of $O(\sqrt{eta})$ on noise for differential privacy.

Stability-enhanced privacy improves utility in elastic nets and feature selection.

Experimental results confirm the practical benefits of stability-based privacy enhancements.

Abstract

Private machine learning involves addition of noise while training, resulting in lower accuracy. Intuitively, greater stability can imply greater privacy and improve this privacy-utility tradeoff. We study this role of stability in private empirical risk minimization, where differential privacy is achieved by output perturbation, and establish a corresponding theoretical result showing that for strongly-convex loss functions, an algorithm with uniform stability of $\beta$ implies a bound of $O(\sqrt{\beta})$ on the scale of noise required for differential privacy. The result applies to both explicit regularization and to implicitly stabilized ERM, such as adaptations of Stochastic Gradient Descent that are known to be stable. Thus, it generalizes recent results that improve privacy through modifications to SGD, and establishes stability as the unifying perspective. It implies new privacy guarantees for optimizations with uniform stability guarantees, where a corresponding differential privacy guarantee was previously not known. Experimental results validate the utility of stability enhanced privacy in several problems, including application of elastic nets and feature selection.