Dimension Independent Generalization of DP-SGD for Overparameterized Smooth Convex Optimization
This work addresses the issue of impractical generalization bounds for overparameterized models in differential privacy, offering a dimension-independent solution that is incremental but impactful for privacy-preserving machine learning applications.
The paper tackles the problem of dimension-dependent generalization bounds in differentially private convex learning for overparameterized models, achieving an optimal excess generalization error of $ ilde{O}(n^{-1/2})$ with $O(n^{-1/4})$ privacy guarantees by leveraging convergence analysis of Langevin algorithms.
This paper considers the generalization performance of differentially private convex learning. We demonstrate that the convergence analysis of Langevin algorithms can be used to obtain new generalization bounds with differential privacy guarantees for DP-SGD. More specifically, by using some recently obtained dimension-independent convergence results for stochastic Langevin algorithms with convex objective functions, we obtain $O(n^{-1/4})$ privacy guarantees for DP-SGD with the optimal excess generalization error of $\tilde{O}(n^{-1/2})$ for certain classes of overparameterized smooth convex optimization problems. This improves previous DP-SGD results for such problems that contain explicit dimension dependencies, so that the resulting generalization bounds become unsuitable for overparameterized models used in practical applications.