Differentially Private Average Consensus with Improved Accuracy-Privacy Trade-off

TL;DR

This work tackles average consensus with differential privacy on initial states in static networks. It introduces a distributed shuffling scheme (DiShuf) based on the Paillier cryptosystem to generate correlated zero-sum randomness, enabling initialization that preserves privacy while allowing almost centralized-level accuracy. By incorporating Gaussian or Laplace noises into the initialization, the proposed DiShuf-based algorithms achieve exponential convergence with a mean-square error that can closely match the centralized DP benchmark, effectively reducing the traditional gap. The approach scales favorably with network size and holds promise for broader applications in privacy-preserving distributed computation.

Abstract

This paper studies the average consensus problem with differential privacy of initial states, for which it is widely recognized that there is a trade-off between the mean-square computation accuracy and privacy level. Considering the trade-off gap between the average consensus algorithm and the centralized averaging approach with differential privacy, we propose a distributed shuffling mechanism based on the Paillier cryptosystem to generate correlated zero-sum randomness. By randomizing each local privacy-sensitive initial state with an i.i.d. Gaussian noise and the output of the mechanism using Gaussian noises, it is shown that the resulting average consensus algorithm can eliminate the gap in the sense that the accuracy-privacy trade-off of the centralized averaging approach with differential privacy can be almost recovered by appropriately designing the variances of the added noises. We also extend such a design framework with Gaussian noises to the one using Laplace noises, and show that the improved privacy-accuracy trade-off is preserved.

Figures (4)

• Figure 1: Trajectories of mean-square computation errors of Algorithm 2, the DPAC-OSP algorithm (\ref{['eq:AveCon']})-\ref{['eq:one-shot']}nozari2017differentially, and the DPCA algorithm \ref{['eq:cent']} with 200 samples
• Figure 2: Trajectories of mean-square computation errors of Algorithm 3, the DPAC-OSP algorithm (\ref{['eq:AveCon']})-\ref{['eq:one-shot']}nozari2017differentially, and the DPCA algorithm \ref{['eq:cent']} with 200 samples
• Figure 3: Box chart of computation errors $\frac{1}{n}\sum_{i=1}^{n}|{x_i}(\infty)-x^\ast|^2$ of our proposed algorithms, the DPCA algorithm and the DPAC-OSP algorithm under different $\epsilon$ with 200 samples
• Figure 4: Box chart of computation errors $\sum_{i=1}^{n}|{x_i}(\infty)-x^\ast|^2$ of our proposed algorithms and the DPAC-OSP algorithm under different $n$ with 200 samples

Theorems & Definitions (16)

• Remark 1
• Proposition 1: Trade-offs of DPAC-OSP algorithm
• Proposition 2: Trade-offs of DPCA algorithm
• Remark 2
• Remark 3
• Remark 4
• Theorem 1: Differential Privacy
• Theorem 2: Convergence
• Theorem 3: Trade-off
• Remark 5