Analyzing the Total Variation of Differentially Private Mechanisms for Improved Privacy Guarantees

Core Concepts

The total variation of a differentially private mechanism can be leveraged to obtain significantly tighter privacy guarantees under composition, compared to standard differential privacy analysis.

Abstract

The paper introduces a refinement to the approximate differential privacy framework by incorporating the notion of "total variation of a mechanism" (denoted by η-TV). This allows for an exact composition result that is shown to be significantly tighter than the optimal bounds for differential privacy alone.
The key contributions are:

Proving an exact composition bound for (ε, δ)-differential privacy coupled with η-TV. This bound can be much tighter than previous results that do not consider the total variation.

Showing that (ε, δ)-DP with η-TV is closed under subsampling, providing a useful property for analyzing algorithms like differentially private stochastic gradient descent.

Computing the total variation of commonly used mechanisms like the Laplace, Gaussian, and staircase mechanisms, and demonstrating connections to previous work.

Analyzing the differentially private stochastic gradient descent algorithm using the refined composition result, showing significant improvements over prior bounds.

Studying the notion of total variation in the local differential privacy setting, and deriving generalized privacy-utility tradeoffs by accounting for both ε-LDP and η-TV constraints.

Stats

The paper does not contain any explicit numerical data or statistics. The key results are theoretical bounds and characterizations related to the composition of differentially private mechanisms with total variation constraints.

Quotes

"The total variation of a differentially private mechanism can be leveraged to obtain significantly tighter privacy guarantees under composition, compared to standard differential privacy analysis."
"We introduce a simple refinement to (approximate) differential privacy that yields better composition results. Namely, we leverage the total variation (TV) of a mechanism, denoted by η-TV, so that we keep track of both the (ε, δ)-parameters for DP and the η-parameter for TV."
"We show that (ε, δ)-DP with η-TV is closed under subsampling (where the mechanism computes the query answer on a random subset of the database)."

Key Insights Distilled From

Total Variation Meets Differential Privacy

by Elena Ghazi,... at arxiv.org 04-30-2024

https://arxiv.org/pdf/2311.01553.pdf

Deeper Inquiries

How can the insights from this work be applied to the design of differentially private machine learning algorithms beyond stochastic gradient descent

The insights from this work can be applied to the design of differentially private machine learning algorithms beyond stochastic gradient descent by providing a framework for analyzing the privacy guarantees of these algorithms. The concept of total variation of a mechanism, in addition to differential privacy parameters, offers a more comprehensive understanding of the privacy properties of the algorithm. By incorporating total variation, designers can achieve tighter composition bounds and better control over the privacy-utility tradeoffs in their algorithms. This can lead to more efficient and effective design choices in ensuring privacy while maintaining utility in machine learning tasks.

What are the implications of the tighter composition bounds on the practical deployment of differentially private systems

The implications of the tighter composition bounds on the practical deployment of differentially private systems are significant. With tighter bounds, system designers and developers can have more confidence in the privacy guarantees provided by their systems. This can lead to increased trust from users and stakeholders, as well as improved compliance with privacy regulations and standards. Additionally, tighter composition bounds can enable more accurate risk assessments and better decision-making in the deployment of differentially private systems. Overall, the tighter bounds enhance the robustness and reliability of the privacy protections offered by these systems.

Can the techniques developed in this work be extended to other privacy notions beyond differential privacy, such as mutual information privacy or Rényi differential privacy

The techniques developed in this work can potentially be extended to other privacy notions beyond differential privacy, such as mutual information privacy or Rényi differential privacy. By adapting the framework to incorporate the specific privacy constraints and properties of these alternative privacy notions, similar analyses and results could be obtained. The concept of total variation and its role in quantifying privacy guarantees can be applied in a broader context to evaluate and enhance the privacy protections offered by systems based on these alternative privacy notions. This extension would contribute to a more comprehensive understanding of privacy in various settings and facilitate the design of privacy-preserving systems across different domains.