为去中心化联邦学习的局部SGD提供精确高斯近似，支持统计推断与安全检测。
Sharp Gaussian approximations for Decentralized Federated Learning
- 提出局部SGD最终迭代的Berry-Esseen定理，实现有效乘子自助法。
- 建立全程轨迹的统一时间高斯近似，可检测对抗攻击。
- 理论结合仿真，适用于隐私保护场景下的模型可靠性分析。
联邦学习在隐私敏感的协作环境中日益流行，局部随机梯度下降（local SGD）是去中心化设置下的关键优化方法。尽管其收敛性已被充分研究，但超越收敛性的渐近统计保证仍有限。本文提出了局部SGD的两种广义高斯近似结果，并探讨其影响：首先，证明了最终局部SGD迭代的Berry-Esseen定理，使得乘子自助法得以有效应用；其次，出于鲁棒性考虑，引入两种不同的时间统一高斯近似，用于整个局部SGD轨迹。这些时间统一近似支持基于高斯自助法的对抗攻击检测测试。通过大量模拟实验验证了理论结果的有效性。
原文摘要 · Abstract (English)
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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