cpSGD: Communication-efficient and differentially-private distributed SGD (1805.10559v1)

Abstract: Distributed stochastic gradient descent is an important subroutine in distributed learning. A setting of particular interest is when the clients are mobile devices, where two important concerns are communication efficiency and the privacy of the clients. Several recent works have focused on reducing the communication cost or introducing privacy guarantees, but none of the proposed communication efficient methods are known to be privacy preserving and none of the known privacy mechanisms are known to be communication efficient. To this end, we study algorithms that achieve both communication efficiency and differential privacy. For $d$ variables and $n \approx d$ clients, the proposed method uses $O(\log \log(nd))$ bits of communication per client per coordinate and ensures constant privacy. We also extend and improve previous analysis of the \emph{Binomial mechanism} showing that it achieves nearly the same utility as the Gaussian mechanism, while requiring fewer representation bits, which can be of independent interest.

• The paper’s main contribution is cpSGD, which cuts per-client communication to O(log log(nd)) bits while maintaining robust differential privacy.
• It refines the Binomial mechanism to achieve utility comparable to the Gaussian mechanism but with a lower communication footprint.
• Methodologically, the work integrates synchronous distributed SGD, gradient quantization, and client-added noise to enable practical federated learning.

Overview of cpSGD: Communication-Efficient and Differentially-Private Distributed SGD

The paper "cpSGD: Communication-efficient and differentially-private distributed SGD" addresses critical challenges in distributed machine learning, specifically focusing on communication efficiency and differential privacy. The motivation stems from scenarios where clients are mobile devices with limited bandwidth and privacy concerns, necessitating solutions that optimize both communication cost and privacy.

Key Contributions

1. Combined Communication Efficiency and Differential Privacy: The paper introduces algorithms that ensure both communication efficiency and differential privacy—two requirements often met separately. For a system with $d$ variables and $n \approx d$ clients, the method significantly reduces communication to $O(\log \log(nd))$ bits per client per coordinate while safeguarding privacy.
2. Analysis of the Binomial Mechanism: The authors enhance the utility analysis of the Binomial mechanism, showing it achieves comparable utility to the Gaussian mechanism but with fewer bits required, presenting a compelling alternative for discrete outputs.

Methodology

• Synchronous Distributed SGD:

The paper details a model where each client updates a local model and communicates gradients. Communication bottleneck issues, particularly significant in federated learning contexts, are addressed using gradient quantization and sparsification strategies.

• Privacy Guarantee Integration:

Existing privacy-preserving algorithms typically induce high communication costs. This paper argues for client-added noise to preserve differential privacy, using cryptographic methods to ensure safety even when a server is untrustworthy.

• Binomial Mechanism:

The proposed approach employs a Binomial distribution for noise addition, capitalizing on its discrete nature for effective quantization. This mechanism is analytically shown to be robust for differential privacy across multiple dimensions.

Numerical Results

The results demonstrate that the proposed algorithms match the privacy and utility of traditional methods like the Gaussian mechanism while substantially reducing the communication costs. For $= O(1)$, the achieved communication is bounded significantly, particularly favoring scenarios with $d \approx n$.

Implications and Future Directions

• Practical Implementations:

With applicability to real-world federated learning scenarios, cpSGD has the potential to facilitate large-scale, private model training with minimal communication overhead.

• Theoretical Advancements:

The analysis of the Binomial mechanism offers theoretical insights that can be generalized to other privacy-preserving techniques, motivating further exploration in privacy-utility trade-offs.

• Future Research:

Potential directions include tightening the analysis of the Binomial mechanism’s efficiency, exploring its integration with advanced optimization algorithms, and assessing broader impacts across different model architectures.

In summary, this paper makes a significant contribution towards seamlessly integrating communication efficiency and differential privacy in distributed SGD, providing both theoretical advancements and practical solutions for federated learning.