Sharp Gaussian Approximations for Decentralized Federated Learning

Abstract

Federated Learning has gained traction in privacy-sensitive collaborative environments, with local SGD emerging as a key optimization method in decentralized settings. While its convergence properties are well-studied, asymptotic statistical guarantees beyond convergence remain limited. In this paper, we present two generalized Gaussian approximation results for local SGD and explore their implications. First, we prove a Berry-Esseen theorem for the final local SGD iterates, enabling valid multiplier bootstrap procedures. Second, motivated by robustness considerations, we introduce two distinct time-uniform Gaussian approximations for the entire trajectory of local SGD. The time-uniform approximations support Gaussian bootstrap-based tests for detecting adversarial attacks. Extensive simulations are provided to support our theoretical results.

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Cite

Text

Bonnerjee et al. "Sharp Gaussian Approximations for Decentralized Federated Learning." Advances in Neural Information Processing Systems, 2025.

Markdown

[Bonnerjee et al. "Sharp Gaussian Approximations for Decentralized Federated Learning." Advances in Neural Information Processing Systems, 2025.](https://mlanthology.org/neurips/2025/bonnerjee2025neurips-sharp/)

BibTeX

@inproceedings{bonnerjee2025neurips-sharp,
  title     = {{Sharp Gaussian Approximations for Decentralized Federated Learning}},
  author    = {Bonnerjee, Soham and Karmakar, Sayar and Wu, Wei Biao},
  booktitle = {Advances in Neural Information Processing Systems},
  year      = {2025},
  url       = {https://mlanthology.org/neurips/2025/bonnerjee2025neurips-sharp/}
}