Dynamic Privacy Budget Allocation Improves Data Efficiency of Differentially Private Gradient Descent

TL;DR

This paper analyzes how dynamic privacy budgets in Differentially Private Gradient Descent can be optimized to improve model utility, providing theoretical insights and empirical validation for different noise schedules and their effects on non-convex losses.

Contribution

It introduces a dynamic noise schedule that minimizes utility loss in DP-GD and explores the effects of momentum and loss curvature on privacy-utility trade-offs.

Findings

Dynamic noise schedules can improve utility in DP-GD.

The influence of noise depends on loss curvature and momentum.

Theoretical analysis links noise influence to optimization performance.

Abstract

Protecting privacy in learning while maintaining the model performance has become increasingly critical in many applications that involve sensitive data. Private Gradient Descent (PGD) is a commonly used private learning framework, which noises gradients based on the Differential Privacy protocol. Recent studies show that \emph{dynamic privacy schedules} of decreasing noise magnitudes can improve loss at the final iteration, and yet theoretical understandings of the effectiveness of such schedules and their connections to optimization algorithms remain limited. In this paper, we provide comprehensive analysis of noise influence in dynamic privacy schedules to answer these critical questions. We first present a dynamic noise schedule minimizing the utility upper bound of PGD, and show how the noise influence from each optimization step collectively impacts utility of the final model. Our study also reveals how impacts from dynamic noise influence change when momentum is used. We empirically show the connection exists for general non-convex losses, and the influence is greatly impacted by the loss curvature.