Sharp Gaussian approximations for Decentralized Federated Learning
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917465412337664 |
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| author | Bonnerjee, Soham Karmakar, Sayar Wu, Wei Biao |
| author_facet | Bonnerjee, Soham Karmakar, Sayar Wu, Wei Biao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp Gaussian approximations for Decentralized Federated Learning Bonnerjee, Soham Karmakar, Sayar Wu, Wei Biao Machine Learning Statistics Theory 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. |
| title | Sharp Gaussian approximations for Decentralized Federated Learning |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2505.08125 |