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Private machine learning involves addition of noise while training, resultingin lower accuracy. Intuitively, greater stability can imply greater privacy andimprove this privacy-utility tradeoff. We study this role of stability inprivate empirical risk minimization, where differential privacy is achieved byoutput perturbation, and establish a corresponding theoretical result showingthat 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 fordifferential privacy.  The result applies to both explicit regularization and to implicitlystabilized ERM, such as adaptations of Stochastic Gradient Descent that areknown to be stable. Thus, it generalizes recent results that improve privacythrough modifications to SGD, and establishes stability as the unifyingperspective. It implies new privacy guarantees for optimizations with uniformstability guarantees, where a corresponding differential privacy guarantee waspreviously not known. Experimental results validate the utility of stabilityenhanced privacy in several problems, including application of elastic nets andfeature selection.

Stability Enhanced Privacy and Applications in Private Stochastic Gradient Descent