Differentially Private Distributed Estimation and Learning: Balancing Privacy and Accuracy in Networked Environments

Core Concepts

The authors propose novel algorithms for distributed estimation and learning that enable networked agents to collectively estimate unknown statistical properties of their privately observed samples while preserving the privacy of their signals and network neighborhoods.

Abstract

The paper introduces differentially private distributed estimation and learning algorithms that enable networked agents to collectively estimate the expected value of sufficient statistics from their privately observed samples, while preserving the privacy of their signals and network neighborhoods. The key highlights and insights are: The authors consider a network of n agents, where each agent observes i.i.d. samples from a common exponential family distribution with an unknown parameter θ. The agents aim to collectively estimate the expected value of the sufficient statistic, mθ = E[ξ(s)], by exchanging information with their neighbors. The authors propose two privacy protection mechanisms: Signal DP, which protects the privacy of the agents' signals, and Network DP, which protects the privacy of the agents' signals and their local neighborhood estimates. For the offline minimum variance unbiased estimation (MVUE) task, the authors show that the optimal noise distribution that minimizes the convergence time under ε-DP constraints is the Laplace distribution with parameters related to the global sensitivity of the sufficient statistic ξ(·) and the network structure. For the online learning of the expected value mθ, the authors derive algorithms that achieve fast convergence rates while satisfying ε-DP constraints. The optimal noise distributions are again shown to be Laplace, with parameters depending on the global sensitivity and the network structure. The authors provide theoretical guarantees on the total error, which is decomposed into the cost of privacy (due to the DP noise) and the cost of decentralization (due to the distributed nature of the problem). Experiments on real-world power grid and household electricity consumption datasets demonstrate the effectiveness of the proposed algorithms in achieving (ε, δ)-DP while not significantly sacrificing convergence compared to non-private baselines.

Stats

∆ = maxs∈S |dξ(s)/ds| is the global sensitivity of the sufficient statistic ξ(·). Mn = maxi∈[n] |ξ(si)| is the maximum absolute value of the sufficient statistics. β⋆ = max{λ2(A), |λn(A)|} is the spectral gap of the doubly-stochastic adjacency matrix A. a = maxi≠j aij is the maximum non-diagonal entry of the adjacency matrix A.

Quotes

"The noise that minimizes the convergence time to the best estimates is the Laplace noise, with parameters corresponding to each agent's sensitivity to their signal and network characteristics." "Our algorithms are amenable to dynamic topologies and balancing privacy and accuracy trade-offs."

Key Insights Distilled From

Differentially Private Distributed Estimation and Learning

by Marios Papac... at arxiv.org 03-29-2024

https://arxiv.org/pdf/2306.15865.pdf

Deeper Inquiries

How can the proposed algorithms be extended to handle non-exponential family distributions or high-dimensional signals

To extend the proposed algorithms to handle non-exponential family distributions or high-dimensional signals, we can adapt the concept of smooth sensitivity. In cases where the global sensitivity is unbounded, the smooth sensitivity approach provides a viable solution. By calculating the smooth sensitivity, we can ensure that the privacy guarantees are maintained even when the global sensitivity is not well-defined. This approach allows for the optimization of noise levels in a way that balances privacy protection and algorithm performance. Additionally, for high-dimensional signals, we can consider the sensitivity of the sufficient statistics in each dimension and adjust the noise levels accordingly to achieve differential privacy while preserving the accuracy of the estimates.

What are the implications of the smooth sensitivity approach when the global sensitivity is unbounded, and how does it affect the performance of the algorithms

The smooth sensitivity approach is particularly useful when the global sensitivity is unbounded. In such cases, relying on the smooth sensitivity allows for a compromise in the differential privacy guarantee by introducing a small information leakage probability. This relaxation of the DP constraint enables the algorithms to handle scenarios where the global sensitivity is not well-defined or is extremely large. While the smooth sensitivity approach may introduce a slight relaxation in the privacy guarantee, it ensures that the algorithms can still provide effective privacy protection while maintaining reasonable accuracy in the estimates. Overall, the smooth sensitivity approach is a valuable tool in scenarios where traditional sensitivity measures are not applicable.

Can the proposed methods be integrated with secure multi-party computation techniques to further enhance privacy guarantees in distributed learning settings

Integrating the proposed methods with secure multi-party computation (SMPC) techniques can further enhance privacy guarantees in distributed learning settings. SMPC allows multiple parties to jointly compute a function over their private inputs without revealing individual inputs to each other. By combining the differential privacy mechanisms with SMPC protocols, we can ensure that the privacy of each party's data is preserved throughout the computation process. This integration adds an extra layer of security and confidentiality, making it more challenging for adversaries to compromise the privacy of the participants' data. By leveraging both differential privacy and SMPC, the proposed algorithms can offer robust privacy protection in distributed learning environments.