Renyi Differential Privacy (1702.07476v3)

Abstract: We propose a natural relaxation of differential privacy based on the Renyi divergence. Closely related notions have appeared in several papers that analyzed composition of differentially private mechanisms. We argue that the useful analytical tool can be used as a privacy definition, compactly and accurately representing guarantees on the tails of the privacy loss. We demonstrate that the new definition shares many important properties with the standard definition of differential privacy, while additionally allowing tighter analysis of composite heterogeneous mechanisms.

• The paper defines R Differential Privacy, leveraging R divergence to refine privacy loss bounds and improve adaptive compositions.
• The paper demonstrates that RDP offers tighter privacy guarantees compared to traditional epsilon-differential privacy.
• The paper establishes advanced composition theorems and validates classic mechanisms, such as Gaussian, under the RDP framework.

Overview of R Differential Privacy

The paper "R\ Differential Privacy" introduces an advanced notion of privacy termed as R differential privacy (RDP), leveraging the R\ divergence to address limitations inherent in standard differential privacy (DP) and its relaxation (-differential privacy. This paper positions RDP as a natural and theoretically sound framework for analyzing the privacy guarantees of algorithms that operate on statistical databases.

Key Contributions

1. Definition of R Differential Privacy: RDP emerges as a refinement over -differential privacy, offering more granular control over the tails of privacy loss distributions. The definition uses the R\ divergence to provide a stricter privacy guarantee that is still compatible with practical compositions of privacy-preserving mechanisms. Notably, RDP permits tighter compositions due to its inherent analytical advantages.
2. Comparison with -Differential Privacy: While -differential privacy allows a bound on the privacy loss for a fraction $\delta$ of the cases, RDP provides a framework compatible with multiple competing privacy guarantees, offering precise tracking of cumulative privacy loss.
3. Properties of RDP: The paper validates that RDP inherits key desirable properties from differential privacy, including robustness to auxiliary information and post-processing immunity. Moreover, RDP enjoys improved bounds under adaptive compositions, an aspect critical for real-world applications involving repetitive use of privacy mechanisms.
4. Advanced Composition Theorem: The research extends the traditional composition theorem, showcasing that RDP can efficiently handle complex compositions of heterogeneous mechanisms without incurring excessive privacy loss. The proposition that RDP mechanisms maintain privacy under adaptive compositions accentuates its utility in dynamic, iterative algorithm settings, such as machine learning models over multiple epochs.
5. Implementation on Basic Mechanisms: The paper analyzes classical privacy mechanisms like Laplace and Gaussian mechanisms under the RDP framework. For instance, the Gaussian mechanism achieves a straightforward RDP budget curve, revealing its theoretical utility while ensuring minimal information leakage.

Implications and Future Directions

The introduction of RDP is significant in aligning privacy enhancements with robust theoretical foundations and practical applications. The work implies that adopting RDP could transform approaches to privacy, especially in scenarios necessitating repeated access or combined data analyses. Practically, RDP facilitates the seamless integration of privacy assurances into iterative processes without undermining the efficacy of the original analyses.

From a theoretical standpoint, RDP challenges conventional beliefs in privacy scope by asserting superiority in cumulative cases over extended interactions with private data. This naturally prompts further examination into alternative divergences or refinements within the RDP framework that might offer specific benefits for specialized applications.

In terms of future developments, extending RDP to formalize privacy guarantees in distributed or federated data mechanisms may prove advantageous, creating avenues for leveraging privacy in increasingly prevalent decentralized data strategies. Moreover, evaluating RDP's impact on broader algorithmic fairness and accountability continues to be an enticing prospect, fostering data-driven innovations under ethical and socially responsible constructs.

Conclusion

This paper's identification of R differential privacy as a concurrent, refined framework signifies a compelling advancement in privacy assessment methodologies. By providing an enhanced lens through the R\ divergence, this work lays the groundwork for more secure, comprehensible privacy protocols capable of adapting to the complexity and diversity of real-world computational environments.