Stability Enhanced Privacy and Applications in Private Stochastic Gradient Descent
This work provides a unifying perspective for improving privacy in stochastic gradient descent and related methods, offering incremental theoretical insights for researchers in private machine learning.
The paper tackles the problem of the privacy-utility tradeoff in private machine learning by showing that greater algorithmic stability can reduce the noise needed for differential privacy, establishing a theoretical bound of O(√β) on noise scale for strongly-convex loss functions with uniform stability β, and validating this with experiments on elastic nets and feature selection.
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 $β$ implies a bound of $O(\sqrtβ)$ 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.