insight - Machine Learning - # Differentially Private Decentralized Stochastic Gradient Push with Variance Reduction

Core Concepts

The proposed PrivSGP-VR algorithm achieves a sub-linear convergence rate of O(1/√nK) under differentially private Gaussian noise, which is independent of stochastic gradient variance and exhibits linear speedup with respect to the number of nodes n. By optimizing the number of iterations K under a given privacy budget, PrivSGP-VR attains a tight utility bound matching that of server-client distributed counterparts, with an extra factor of 1/√n improvement compared to existing decentralized algorithms.

Abstract

The paper proposes a differentially private decentralized learning method called PrivSGP-VR, which employs stochastic gradient push with variance reduction to solve non-convex optimization problems over time-varying directed communication graphs.
Key highlights:
PrivSGP-VR guarantees (ϵ, δ)-differential privacy for each node, by injecting Gaussian noise into the local stochastic gradients.
Theoretical analysis shows that PrivSGP-VR achieves a sub-linear convergence rate of O(1/√nK), which is independent of stochastic gradient variance and scales linearly with the number of nodes n.
By leveraging the moments accountant method, the authors derive an optimal number of iterations K to maximize the model utility under a given privacy budget (ϵ, δ) for each node.
With the optimized K, PrivSGP-VR achieves a tight utility bound of O(√(d log(1/δ))/(√nJϵ)), which matches that of server-client distributed counterparts and exhibits an extra factor of 1/√n improvement compared to existing decentralized algorithms.
Extensive experiments on CNN and shallow neural network training tasks validate the theoretical findings, especially the existence of an optimal K that maximizes the model utility under a certain privacy budget.

Stats

The stochastic gradient is bounded as ∥∇fi(x; ξi)∥ ≤ G.
The smoothness parameter L = 25.
The bounded data heterogeneity parameter b^2 = 500000.
The initial objective value f(x^0) - f* = 2.8.
The initial model parameter norm ∥x^0∥^2 = 780000.

Quotes

"Given certain privacy budget (ϵi, δi) for each node i, there exists an optimal value of K that minimizes the error bound and thus maximizes the model accuracy."
"As the privacy budget ϵ diminishes (indicating a higher level of privacy protection), the maximized model utility deteriorates."

Key Insights Distilled From

by Zehan Zhu,Ya... at **arxiv.org** 05-07-2024

Deeper Inquiries

To extend the PrivSGP-VR algorithm to handle non-i.i.d. data distributions across nodes, we can introduce personalized privacy budgets for each node based on the characteristics of their local data. This means that each node will have its own unique privacy parameters (ϵi, δi) tailored to the distribution of its data. By incorporating node-specific privacy budgets, the algorithm can adapt to the varying data distributions and ensure differential privacy guarantees for each node. Additionally, we can explore techniques such as data preprocessing, data augmentation, or federated learning approaches to address the challenges posed by non-i.i.d. data distributions in a decentralized setting.

The moments accountant method, while effective in providing accurate estimates of privacy loss, may have limitations in certain scenarios. One potential limitation is the assumption of independent noise addition at each iteration, which may not hold true in practice. This can lead to underestimation or overestimation of the privacy loss. To address this limitation, alternative privacy analysis techniques such as Renyi differential privacy or concentrated differential privacy can be incorporated. These methods offer different trade-offs in terms of accuracy and computational complexity, providing a more robust framework for estimating privacy loss in decentralized learning settings. By combining multiple privacy analysis techniques and conducting sensitivity analysis, we can enhance the accuracy and reliability of privacy guarantees in the PrivSGP-VR framework.

The PrivSGP-VR framework can be adapted to various decentralized optimization problems beyond machine learning, such as resource allocation or multi-agent coordination tasks. By modifying the loss function and gradient computation to suit the specific optimization problem, the algorithm can be applied to tasks like decentralized resource management, task allocation, or collaborative decision-making. For resource allocation, nodes can optimize their local decisions while ensuring privacy and coordination with other nodes. In multi-agent coordination tasks, the algorithm can facilitate collaborative learning and decision-making among agents while preserving individual privacy. By customizing the objective function and communication protocols, the PrivSGP-VR framework can be tailored to a wide range of decentralized optimization problems, offering privacy guarantees and efficient convergence in diverse applications.

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