Federated learning with heavy-tailed gradient noise and communication noise: a variance-reduction based algorithm

• URL: http://arxiv.org/abs/2606.22466v1
• Date: Sun, 21 Jun 2026 12:18:43 GMT
• Title: Federated learning with heavy-tailed gradient noise and communication noise: a variance-reduction based algorithm
• Abstract summary: Federated learning (FL) is an emerging distributed machine learning paradigm that enables local devices to jointly train a global model while keeping data decentralized and private.<n>We propose a convex-tailed noise-reduction based algorithm, VRA-FedSGD, for FL in the context of heavy communication noise over wireless Internet of Things networks.<n>VRA-FedSGD employs momentum reduction together with a reduction-reduced aggregation mechanism to suppress heavy communication noise.
• Score: 7.852384021898989
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Federated learning (FL) is an emerging distributed machine learning paradigm that enables local devices to jointly train a global model while keeping data decentralized and private. We propose a variance-reduction based algorithm, VRA-FedSGD, for FL in the presence of heavy-tailed gradient noise and communication noise, where these noises are prevalent in large-scale machine learning over wireless networks and Internet of Things deployments. VRA-FedSGD employs a momentum variance reduction technique together with a nonlinear mapping to mitigate heavy-tailed gradient noise, and uses a variance-reduced aggregation mechanism to suppress heavy-tailed communication noise. In the mean sense, VRA-FedSGD achieves a convergence rate of {\small$\mathcal{O}\left(K^{-(p-1)/(2p-1)}\right)$} for nonconvex objective functions, where $p$ is the tail index of heavy-tailed noise. In the almost sure sense, VRA-FedSGD achieves a convergence rate of $\tilde{\mathcal{O}}\left(K^{-(1-1/(p-ε))}\right)$ for strongly convex objective functions, where $ε$ is an arbitrarily small constant. Simulated experiments on a logistic regression problem with real-world data verify the effectiveness of VRA-FedSGD.

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