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<p>In recent years, federated learning (FL) has emerged as a prominent paradigm in distributed optimization for operations research and machine learning. Despite the partial safeguarding of agents’ information within FL systems, a malicious adversary can potentially infer sensitive information through various means. In this paper, we propose a generic private FL framework defined on Riemannian manifolds (PriRFed) based on the differential privacy (DP) technique. One of the key challenges, averaging different points in a manifold, is addressed with retraction and its inverse. We analyze the privacy guarantee while establishing the convergence properties. To the best of our knowledge, this is the first federated learning framework on Riemannian manifold with a privacy guarantee and convergence results. Numerical simulations are performed on synthetic and real-world datasets to showcase the efficacy of the proposed PriRFed approach.</p>

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Federated Learning on Riemannian Manifolds with Differential Privacy

  • 期刊论文

  • 发表日期：

    2026年4月2日

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  • Zhenwei Huang,
  • Wen Huang,
  • Pratik Jawanpuria,
  • Bamdev Mishra

摘要

In recent years, federated learning (FL) has emerged as a prominent paradigm in distributed optimization for operations research and machine learning. Despite the partial safeguarding of agents’ information within FL systems, a malicious adversary can potentially infer sensitive information through various means. In this paper, we propose a generic private FL framework defined on Riemannian manifolds (PriRFed) based on the differential privacy (DP) technique. One of the key challenges, averaging different points in a manifold, is addressed with retraction and its inverse. We analyze the privacy guarantee while establishing the convergence properties. To the best of our knowledge, this is the first federated learning framework on Riemannian manifold with a privacy guarantee and convergence results. Numerical simulations are performed on synthetic and real-world datasets to showcase the efficacy of the proposed PriRFed approach.