Improved Communication-Privacy Trade-offs in $L_2$ Mean Estimation under Streaming Differential Privacy

TL;DR

This paper introduces a novel privacy accounting method for $L_2$ mean estimation under streaming differential privacy, achieving near-optimal mean square errors and significant compression improvements in federated learning tasks.

Contribution

It presents a new privacy accounting technique for sparsified Gaussian mechanisms directly in $L_2$ geometry and extends it to matrix factorization under streaming DP, improving efficiency and compatibility.

Findings

Achieves at least 100x compression improvement for DP-SGD in federated learning.

Provides a privacy accountant that directly operates in $L_2$ geometry, reducing MSEs.

Extends sparsification schemes to matrix factorization under streaming DP.

Abstract

We study $L_2$ mean estimation under central differential privacy and communication constraints, and address two key challenges: firstly, existing mean estimation schemes that simultaneously handle both constraints are usually optimized for $L_\infty$ geometry and rely on random rotation or Kashin's representation to adapt to $L_2$ geometry, resulting in suboptimal leading constants in mean square errors (MSEs); secondly, schemes achieving order-optimal communication-privacy trade-offs do not extend seamlessly to streaming differential privacy (DP) settings (e.g., tree aggregation or matrix factorization), rendering them incompatible with DP-FTRL type optimizers. In this work, we tackle these issues by introducing a novel privacy accounting method for the sparsified Gaussian mechanism that incorporates the randomness inherent in sparsification into the DP noise. Unlike previous approaches, our accounting algorithm directly operates in $L_2$ geometry, yielding MSEs that fast converge to those of the uncompressed Gaussian mechanism. Additionally, we extend the sparsification scheme to the matrix factorization framework under streaming DP and provide a precise accountant tailored for DP-FTRL type optimizers. Empirically, our method demonstrates at least a 100x improvement of compression for DP-SGD across various FL tasks.