The Relative Gaussian Mechanism and its Application to Private Gradient Descent

Core Concepts

Relative L2 sensitivity assumption allows for adaptive noise levels in the Relative Gaussian Mechanism, ensuring privacy in gradient descent.

Abstract

The content introduces the concept of Relative L2 Sensitivity, presents the Relative Gaussian Mechanism (RGMγ,σ) for private gradient descent, and discusses enforcing relative sensitivity through clipping features and Propose-Test-Release (PTR). Experimental results on linear regression datasets illustrate the effectiveness of RGM compared to traditional gradient clipping methods. 1. Introduction Gaussian Mechanism (GM) adds noise to protect privacy. Challenges with precise L2 sensitivity lead to loose privacy bounds. Introducing Relative L2 sensitivity assumption for adaptive noise levels in RGM. 2. Differential Privacy Concepts Rényi Differential Privacy (RDP) based on Rényi divergence. GMσ used in differentially private algorithms like gradient descent. Importance of accurately estimating sensitivity for optimal privacy-utility trade-off. 3. Theoretical Framework Definition of Relative L2 Sensitivity for queries dependent on norm. Introduction of Relative Gaussian Mechanism (RGMγ,σ) with adaptive noise variance. 4. Privacy Guarantees and Comparison Tight bounds on RDP parameters using RGM under relative sensitivity assumption. Comparison with standard GMσ mechanism and implications for utility and privacy trade-offs. 5. Practical Implementation Enforcing relative sensitivity through clipping features and PTR framework. Experimental results showing effectiveness of RGM compared to traditional clipping methods in linear regression tasks.

Stats

In particular, we show that RGM naturally adapts to a latent variable that would control the norm of the output.

Quotes

"RDP is able to tightly track the privacy guarantees of GMσ." "We introduce the Relative L2 Sensitivity, which generalizes the L2 sensitivity by allowing the upper bound to depend on the norm of queries."

Key Insights Distilled From

The Relative Gaussian Mechanism and its Application to Private Gradient Descent

by Hadr... at arxiv.org 03-20-2024

https://arxiv.org/pdf/2308.15250.pdf

Deeper Inquiries

How can relative sensitivity assumptions be extended beyond Gaussian noise?

Relative sensitivity assumptions can be extended beyond Gaussian noise by considering different types of noise distributions that capture the specific characteristics of the data and query being analyzed. One approach is to explore non-Gaussian noise models, such as Laplace or Exponential distributions, which may better align with the underlying structure of the data. By incorporating these alternative noise models into the relative sensitivity framework, it becomes possible to adapt the level of privacy protection based on a more nuanced understanding of how different types of noise affect the release of information.

What are the implications of enforcing relative sensitivity through clipping features?

Enforcing relative sensitivity through clipping features has several implications for differential privacy mechanisms. Firstly, it allows for a more tailored and adaptive approach to setting privacy parameters based on the specific characteristics of each dataset or query. By using clipping thresholds that are determined locally and reflect the distribution of individual gradients or outputs, it becomes possible to achieve tighter bounds on privacy guarantees without sacrificing utility. Additionally, utilizing clipping features in conjunction with relative sensitivity helps address challenges related to setting global thresholds for absolute sensitivities. This localized approach reduces communication overhead between nodes in distributed settings and minimizes potential leakage from sharing sensitive information needed to set global thresholds accurately. Overall, enforcing relative sensitivity through clipping features enhances both the effectiveness and efficiency of differential privacy mechanisms by providing a flexible and data-driven method for ensuring robust privacy protections while maintaining utility in various applications.

How does PTR framework impact practical implementation of differential privacy mechanisms?

The Propose-Test-Release (PTR) framework significantly impacts practical implementations of differential privacy mechanisms by offering a systematic way to evaluate and enforce local sensitivities without requiring extensive communication or sharing sensitive information across nodes. One key impact is that PTR enables nodes in distributed systems to independently test their datasets against predefined criteria for satisfying certain levels of local sensitivities before engaging in collaborative tasks like gradient descent optimization. This decentralized testing process reduces reliance on centralized decision-making regarding parameter settings like clipping thresholds or noise levels, thereby enhancing scalability and preserving individual data confidentiality within each node's domain. Moreover, PTR facilitates efficient tuning and adjustment during model training by allowing nodes to iteratively propose candidate solutions (e.g., values for parameters like ρ) based on local computations without compromising overall system security or performance. This iterative nature ensures that only viable options meeting specified conditions are further considered for implementing differential privacy measures effectively across all participating entities. In essence, by streamlining validation procedures while upholding stringent standards for safeguarding private information exchange among networked components, PTR contributes towards establishing robust yet agile frameworks for deploying differential privacy safeguards in real-world scenarios where data confidentiality is paramount.