Improving Differentially Private SGD via Randomly Sparsified Gradients

TL;DR

This paper introduces a random sparsification technique for DP-SGD that improves privacy, reduces communication costs, and enhances performance by leveraging the unique properties of gradient compression in differentially private deep learning.

Contribution

It proposes a novel random sparsification extension to DP-SGD, demonstrating theoretical benefits and empirical improvements in privacy, efficiency, and model performance.

Findings

Random sparsification improves DP-SGD performance.

Sparse gradients reduce communication costs.

Sparse gradients enhance privacy against reconstruction attacks.

Abstract

Differentially private stochastic gradient descent (DP-SGD) has been widely adopted in deep learning to provide rigorously defined privacy, which requires gradient clipping to bound the maximum norm of individual gradients and additive isotropic Gaussian noise. With analysis of the convergence rate of DP-SGD in a non-convex setting, we identify that randomly sparsifying gradients before clipping and noisification adjusts a trade-off between internal components of the convergence bound and leads to a smaller upper bound when the noise is dominant. Additionally, our theoretical analysis and empirical evaluations show that the trade-off is not trivial but possibly a unique property of DP-SGD, as either canceling noisification or gradient clipping eliminates the trade-off in the bound. This observation is indicative, as it implies DP-SGD has special inherent room for (even simply random) gradient compression. To verify the observation and utilize it, we propose an efficient and lightweight extension using random sparsification (RS) to strengthen DP-SGD. Experiments with various DP-SGD frameworks show that RS can improve performance. Additionally, the produced sparse gradients of RS exhibit advantages in reducing communication cost and strengthening privacy against reconstruction attacks, which are also key problems in private machine learning.