Differentially Private Distributed Stochastic Optimization with Time-Varying Sample Sizes: Privacy Protection in Optimization

Core Concepts

Efficiently achieving differential privacy and convergence in distributed stochastic optimization.

Abstract

The urgent need for privacy protection in distributed stochastic optimization has led to the development of algorithms that ensure both convergence and differential privacy. This paper proposes two-time scale stochastic approximation-type algorithms for differentially private distributed stochastic optimization with time-varying sample sizes. By incorporating gradient- and output-perturbation methods, the algorithm enhances privacy levels while guaranteeing convergence rates. The mean-square convergence rates are rigorously provided, showcasing the impact of added privacy noise on algorithm performance. Numerical examples demonstrate the efficiency and advantages of the proposed algorithms, particularly in scenarios like distributed training on machine learning datasets.

Stats

"The undirected communication topology G is connected, and the adjacency matrix A satisfies certain conditions."
"For any i P V, each function ∇fi is Lipschitz continuous."
"There exists a positive constant η such that aij ą η for j P Ni."

Quotes

"The main contributions of this paper are summarized as follows: A differentially private distributed stochastic optimization algorithm with time-varying sample sizes is presented for both output- and gradient-perturbation cases." - Authors

Key Insights Distilled From

Differentially Private Distributed Stochastic Optimization with Time-Varying Sample Sizes

by Jimin Wang,J... at arxiv.org 03-19-2024

https://arxiv.org/pdf/2310.11892.pdf

Deeper Inquiries

How can differential privacy be balanced with accuracy in distributed stochastic optimization

In distributed stochastic optimization, balancing differential privacy with accuracy is crucial for ensuring the protection of sensitive information while maintaining the effectiveness of the optimization process. One way to achieve this balance is by carefully selecting parameters such as step sizes, noise levels, and sample sizes in the algorithm design. By optimizing these parameters based on the specific requirements of the application and considering trade-offs between privacy and accuracy, it is possible to strike a balance that meets both objectives.
Additionally, utilizing techniques like time-varying sample sizes can help enhance privacy protection without significantly compromising accuracy. This method allows for processing multiple samples at each iteration, reducing sensitivity to individual data points while still achieving convergence towards optimal solutions. By incorporating differential privacy mechanisms into distributed stochastic optimization algorithms effectively, it becomes feasible to maintain a high level of privacy protection without sacrificing too much in terms of accuracy.

What are the implications of increasing variance in added privacy noise on algorithm performance

The increasing variance in added privacy noise can have significant implications on algorithm performance in distributed stochastic optimization. As the variance of the noise grows larger, it introduces more uncertainty into the gradient estimates used for optimization. This increased uncertainty can lead to higher levels of distortion in the computed gradients, potentially affecting convergence rates and solution quality.
Higher variance in added privacy noise may result in greater perturbations to gradient updates during each iteration, leading to slower convergence or suboptimal solutions. The trade-off between preserving differential privacy and maintaining accurate estimation becomes more pronounced as noise variance increases since excessive noise can overshadow useful signal information from data samples.
To mitigate these implications, careful calibration of noise levels based on sensitivity analysis and understanding their impact on algorithm performance is essential. Balancing the amount of added noise with its effect on convergence rates and solution quality is crucial for optimizing algorithm performance under varying degrees of privacy constraints.

How does the concept of differential privacy extend to other fields beyond optimization

Differential privacy extends beyond just optimization into various other fields where safeguarding sensitive information is paramount. In machine learning applications like deep learning models trained on private datasets or federated learning setups involving multiple parties sharing data collaboratively but privately—differential privacy ensures that individual contributions remain confidential while still contributing meaningfully to model training.
Moreover, differential privacy finds applications in healthcare systems where patient data must be protected against unauthorized access or inference attempts by malicious actors seeking personal information from medical records or diagnostic reports shared among healthcare providers securely using encryption methods combined with differential private mechanisms.
In financial services industries handling transactional data or customer profiles containing sensitive details—differential privacy safeguards against potential breaches or leaks that could compromise individuals' financial security or expose proprietary business insights through secure computation protocols ensuring confidentiality while enabling collaborative analytics across institutions securely.