Amplifying Privacy Guarantees for Matrix Mechanisms via Conditional Composition

核心概念

This work proposes a generic privacy amplification algorithm, MMCC, that can analyze the privacy guarantees of any matrix mechanism, including state-of-the-art DP-FTRL algorithms, by leveraging conditional composition and mixture of Gaussians mechanisms.

要約

The paper presents a novel privacy amplification analysis for matrix mechanisms, which are a class of differentially private algorithms used in machine learning. The key contributions are:

1. Conditional Composition Theorem: The authors prove a conditional composition theorem that allows analyzing a sequence of adaptive mechanisms using high-probability instead of worst-case privacy guarantees for each mechanism. This generalizes previous ideas used to analyze amplification by shuffling.

2. MMCC Algorithm: The authors propose the MMCC algorithm, which computes nearly-tight amplified privacy guarantees for any matrix mechanism with uniform sampling. MMCC approaches a lower bound as the privacy parameter ε approaches 0.

3. Binary Tree Analysis: The authors show that the binary tree DP-FTRL mechanism can asymptotically match the noise added to DP-SGD with amplification, by leveraging the versatility of the conditional composition theorem.

4. Empirical Improvements: The authors demonstrate significant empirical improvements in the privacy-utility tradeoffs for DP-FTRL algorithms on standard benchmarks, by applying the MMCC analysis.

The paper tackles the challenge that standard privacy amplification analysis does not directly apply to matrix mechanisms, as the noise added to each row is correlated. The authors overcome this by reducing the analysis to a sequence of mixture of Gaussians mechanisms, which can be analyzed using their conditional composition theorem.

統計

The paper does not contain any explicit numerical data or statistics. It focuses on theoretical analysis and algorithmic contributions.

引用

"Privacy amplification exploits randomness in data selection to provide tighter differential privacy (DP) guarantees. This analysis is key to DP-SGD's success in machine learning (ML), but, is not readily applicable to the newer state-of-the-art (SOTA) algorithms."
"Bringing privacy amplification to matrix mechanisms (MMs) is an important area of research to enable better privacy-utility tradeoffs."
"Our main contribution is to prove a general privacy amplification analysis for any matrix mechanism, i.e., arbitrary encoder matrices C for non-adaptively chosen x, and for lower-triangular C's when x is adaptively chosen (which is the typical situation for machine learning tasks)."

抽出されたキーインサイト

Privacy Amplification for Matrix Mechanisms

by Christopher ... 場所 arxiv.org 05-07-2024

https://arxiv.org/pdf/2310.15526.pdf

深掘り質問

How can the conditional composition theorem be applied to analyze other correlated noise mechanisms beyond matrix mechanisms

The conditional composition theorem can be applied to analyze other correlated noise mechanisms beyond matrix mechanisms by adapting the same principles used in the analysis of matrix mechanisms. The key idea is to break down the mechanism into smaller components, where each component's output is conditioned on the outputs of the previous components. By establishing dominance relationships between these components, it is possible to analyze the overall mechanism's privacy guarantees using high-probability bounds rather than worst-case scenarios. This approach allows for a more nuanced and accurate analysis of the privacy implications of correlated noise mechanisms.

What are the limitations of the current amplification by shuffling results, and can they be improved to further tighten the binary tree mechanism analysis

The current amplification by shuffling results has limitations in terms of the scalability and applicability to more complex mechanisms. One limitation is the requirement for a large number of samples (n = Ω(log 1/δ)) to achieve optimal noise levels in the binary tree mechanism analysis. This limitation restricts the practicality of the analysis for smaller datasets or scenarios where a large number of samples is not feasible. To improve the analysis and tighten the bounds for the binary tree mechanism, research could focus on developing more efficient amplification techniques that reduce the dependency on the number of samples required for accurate analysis. By addressing these limitations, the analysis of the binary tree mechanism can be enhanced to provide more precise privacy guarantees across a wider range of scenarios.

Can the mixture of Gaussians mechanism analysis be extended to handle more general noise distributions beyond the Gaussian case

The mixture of Gaussians mechanism analysis can be extended to handle more general noise distributions beyond the Gaussian case by adapting the framework to accommodate different probability distributions and sensitivity measures. By incorporating the characteristics of the specific noise distribution into the analysis, it is possible to derive privacy guarantees tailored to the unique properties of the noise model. This extension would involve defining the probabilities and sensitivities based on the parameters of the alternative noise distribution and establishing dominance relationships to ensure accurate and reliable privacy analysis. By expanding the scope of the mixture of Gaussians mechanism analysis, researchers can provide comprehensive privacy assessments for a broader range of noise models used in differential privacy mechanisms.