[Paper Review] Privacy Preserving Randomized Gossip Algorithms

Filip Hanzely, Jakub Konečný+3 more|arXiv (Cornell University)|Jun 23, 2017

Distributed Control Multi-Agent Systems44 references16 citations

TL;DR

This paper proposes three novel randomized gossip algorithms that preserve privacy in distributed average consensus by either weakening value-oracle access or injecting controlled noise during iterations. The methods ensure convergence to the true average while significantly reducing the risk of inferring initial private values, with theoretical convergence rates and empirical validation on various network topologies.

ABSTRACT

In this work we present three different randomized gossip algorithms for solving the average consensus problem while at the same time protecting the information about the initial private values stored at the nodes. We give iteration complexity bounds for all methods, and perform extensive numerical experiments.

Motivation & Objective

• To address the challenge of protecting private initial values in distributed average consensus protocols.
• To design gossip algorithms that prevent nodes from learning sensitive information about others' initial values.
• To maintain convergence to the true average while enhancing privacy through algorithmic modifications.
• To provide theoretical convergence rates and empirical validation on common network topologies.

Proposed method

• Introduces a private variant of the randomized pairwise gossip algorithm that limits information exchange to categorical or binary responses about neighboring node values.
• Proposes a noise injection mechanism where random noise is added and gradually withdrawn during iterations to obscure initial values.
• Uses a decay rate parameter φi for each node to control the rate of noise withdrawal, ensuring convergence to the average.
• Employs a theoretical framework to derive convergence rates dependent on network structure and noise parameters.
• Applies the methods to cycle and random geometric graphs, comparing performance under varying noise decay rates.
• Uses a noise oracle that dynamically adjusts noise levels based on node degree and network topology.

Experimental results

Research questions

• RQ1 How can randomized gossip algorithms be modified to protect the privacy of initial values in distributed average consensus?
• RQ2 What is the impact of controlled noise injection on convergence speed and privacy preservation?
• RQ3 Can restricting the information returned by the value oracle enhance privacy without sacrificing convergence?
• RQ4 What is the optimal decay rate of noise for balancing privacy and convergence speed?
• RQ5 How does node-specific noise decay (φi) affect performance compared to uniform decay?

Key findings

• The proposed private gossip algorithms converge to the true average consensus value while significantly reducing the risk of inferring initial private values.
• Noise injection with node-specific decay rates φi allows for higher overall noise levels without degrading convergence, improving privacy.
• When φi is chosen according to Corollary 12, the practical convergence rate closely matches theoretical predictions.
• The histogram of φi values shows that most nodes can tolerate higher noise levels than the minimum required, enabling stronger privacy protection.
• For random geometric graphs, the method with adaptive φi outperforms uniform decay in both convergence speed and noise resilience.
• Theoretical convergence rates are derived and validated empirically, showing that noise-dominated regimes emerge beyond a critical threshold of φi.