Near Exact Privacy Amplification for Matrix Mechanisms

TL;DR

This paper introduces a near-exact framework for computing privacy parameters in differential privacy mechanisms with correlated noise, enabling optimized privacy amplification and improved performance in machine learning tasks.

Contribution

It provides a novel framework for calculating near-exact privacy parameters for any lower-triangular correlation matrix, allowing optimization of privacy amplification.

Findings

Achieves smaller RMSE on prefix sums than previous methods

Improves deep learning task performance with optimized privacy parameters

Uses Monte Carlo accounting and a new batching scheme for better privacy analysis

Abstract

We study the problem of computing the privacy parameters for DP machine learning when using privacy amplification via random batching and noise correlated across rounds via a correlation matrix $\textbf{C}$ (i.e., the matrix mechanism). Past work on this problem either only applied to banded $\textbf{C}$, or gave loose privacy parameters. In this work, we give a framework for computing near-exact privacy parameters for any lower-triangular, non-negative $\textbf{C}$. Our framework allows us to optimize the correlation matrix $\textbf{C}$ while accounting for amplification, whereas past work could not. Empirically, we show this lets us achieve smaller RMSE on prefix sums than the previous state-of-the-art (SOTA). We also show that we can improve on the SOTA performance on deep learning tasks. Our two main technical tools are (i) using Monte Carlo accounting to bypass composition, which was the main technical challenge for past work, and (ii) a "balls-in-bins" batching scheme that enables easy privacy analysis and is closer to practical random batching than Poisson sampling.