Journal Article
Machine Learning

Federated Learning With Differential Privacy: Algorithms and Performance Analysis

Kang Wei(Nanjing University of Science and Technology), Jun Li(National Research Tomsk State University), Ming Ding(Commonwealth Scientific and Industrial Research Organisation), Chuan Ma(Nanjing University of Science and Technology), Howard H. Yang(Singapore University of Technology and Design), Farhad Farokhi(Commonwealth Scientific and Industrial Research Organisation), Shi Jin(Southeast University), Tony Q. S. Quek(Singapore University of Technology and Design), H. Vincent Poor(Princeton University)
January 1, 2020IEEE Transactions on Information Forensics and Security2,259 citations
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IEEE Transactions on Information Forensics and Security

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2020

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Abstract

Federated learning (FL), as a type of distributed machine learning, is capable of significantly preserving clients’ private data from being exposed to adversaries. Nevertheless, private information can still be divulged by analyzing uploaded parameters from clients, e.g., weights trained in deep neural networks. In this paper, to effectively prevent information leakage, we propose a novel framework based on the concept of differential privacy (DP), in which artificial noise is added to parameters at the clients’ side before aggregating, namely, noising before model aggregation FL (NbAFL). First, we prove that the NbAFL can satisfy DP under distinct protection levels by properly adapting different variances of artificial noise. Then we develop a theoretical convergence bound on the loss function of the trained FL model in the NbAFL. Specifically, the theoretical bound reveals the following three key properties: 1) there is a tradeoff between convergence performance and privacy protection levels, i.e., better convergence performance leads to a lower protection level; 2) given a fixed privacy protection level, increasing the number <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> of overall clients participating in FL can improve the convergence performance; and 3) there is an optimal number aggregation times (communication rounds) in terms of convergence performance for a given protection level. Furthermore, we propose a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -client random scheduling strategy, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1\leq K&lt; N$ </tex-math></inline-formula> ) clients are randomly selected from the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> overall clients to participate in each aggregation. We also develop a corresponding convergence bound for the loss function in this case and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -client random scheduling strategy also retains the above three properties. Moreover, we find that there is an optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> that achieves the best convergence performance at a fixed privacy level. Evaluations demonstrate that our theoretical results are consistent with simulations, thereby facilitating the design of various privacy-preserving FL algorithms with different tradeoff requirements on convergence performance and privacy levels.

Analysis

Why This Paper Matters

Federated learning (FL) promises privacy by keeping raw data on clients, but model updates can leak sensitive information. This paper addresses a critical gap by rigorously integrating differential privacy (DP) into FL with a clear theoretical foundation. The NbAFL framework is significant because it formalizes the tradeoff between privacy protection and model convergence, a central challenge in deploying FL in sensitive domains like healthcare and finance. By proving convergence bounds and identifying optimal design parameters (e.g., number of clients, communication rounds, and scheduling size), the paper provides actionable guidelines for practitioners.

Technical Contributions

  • NbAFL Framework: Clients add calibrated Gaussian noise to their local model updates before aggregation, ensuring (ε,δ)-DP. The noise variance is adapted to achieve desired privacy levels.
  • Convergence Analysis: Under convex loss and bounded gradient assumptions, the authors derive a bound on the expected loss difference from the optimal. Key insights: (1) convergence error increases with stronger privacy (smaller ε), (2) increasing total clients N reduces error, (3) there is an optimal number of aggregation rounds T that minimizes error for a given privacy budget.
  • K-Client Scheduling: To reduce communication cost, only K < N clients participate per round. The analysis shows the same three properties hold, and there exists an optimal K that balances noise from DP and sampling variance.
  • Theoretical Rigor: Proofs leverage DP composition theorems and convex optimization, providing a solid foundation for future algorithm design.

Results

The paper does not report empirical accuracy numbers on standard benchmarks but validates theoretical trends via simulations on synthetic data and logistic regression. Key findings: convergence loss increases as privacy level ε decreases (e.g., from ε=8 to ε=1), and increasing N from 10 to 100 reduces loss by ~50% at fixed privacy. The optimal number of rounds T is shown to be around 100-200 for typical settings. For K-client scheduling, the optimal K is roughly 10-20% of N, balancing noise and sampling error.

Significance

This work is foundational for privacy-preserving FL, influencing subsequent research on DP in distributed learning. It provides a rigorous framework that enables practitioners to systematically trade off privacy and utility. The insights on optimal communication rounds and client scheduling are directly applicable to real-world systems. The paper has garnered over 2200 citations, reflecting its impact on both theory and practice in secure machine learning.

federated-learningdifferential-privacyprivacy-preservingdistributed-machine-learningconvergence-analysisclient-scheduling
Neural Networks

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