Dimension Independent Generalization of DP-SGD for Overparameterized Smooth Convex Optimization

TL;DR

This paper introduces a dimension-independent analysis of DP-SGD, providing improved generalization bounds for overparameterized smooth convex optimization, leveraging Langevin algorithm convergence results.

Contribution

It develops a new dimension-independent convergence analysis for DP-SGD, leading to tighter generalization bounds applicable to overparameterized models.

Findings

Achieves $O(n^{-1/4})$ privacy guarantees.

Attains $ ilde{O}(n^{-1/2})$ excess generalization error.

Improves upon previous dimension-dependent DP-SGD bounds.

Abstract

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.