Gradient Perturbation is Underrated for Differentially Private Convex Optimization
This work provides a theoretical justification for gradient perturbation in privacy-preserving optimization, potentially benefiting applications requiring secure data analysis.
The paper tackles the problem of differentially private convex optimization by analyzing how privacy noise affects optimization properties, showing that gradient perturbation achieves a significantly improved utility guarantee based on expected curvature rather than minimum curvature, with experiments confirming large performance margins over other methods.
Gradient perturbation, widely used for differentially private optimization, injects noise at every iterative update to guarantee differential privacy. Previous work first determines the noise level that can satisfy the privacy requirement and then analyzes the utility of noisy gradient updates as in the non-private case. In contrast, we explore how privacy noise affects optimization property. We show that for differentially private convex optimization, the utility guarantee of differentially private (stochastic) gradient descent is determined by an \emph{expected curvature} rather than the minimum curvature. The \emph{expected curvature}, which represents the average curvature over the optimization path, is usually much larger than the minimum curvature. By using the \emph{expected curvature}, we show that gradient perturbation can achieve a significantly improved utility guarantee that can theoretically justify the advantage of gradient perturbation over other perturbation methods. Finally, our extensive experiments suggest that gradient perturbation with the advanced composition method indeed outperforms other perturbation approaches by a large margin, matching our theoretical findings.