提出FedNMap算法，实现非凸联邦学习的线性加速。
Achieving Linear Speedup for Composite Federated Learning
- 基于法向映射更新，处理非光滑正则项
- 在非凸损失下，客户端数和本地迭代数均实现线性加速
- 适合数据异质性强的联邦学习场景
本文提出FedNMap，一种用于复合联邦学习的法向映射方法，其目标函数包含平滑损失与可能非光滑的正则项。该方法采用基于法向映射的更新机制处理非光滑项，并引入局部校正策略缓解客户端间数据异质性的影响。在标准假设下——包括局部损失平滑、正则项弱凸性以及有界随机梯度方差——FedNMap在非凸损失情况下，无论是否满足Polyak-Łojasiewicz条件，均实现了关于客户端数量和本地更新次数的线性加速。据我们所知，这是首个在非凸复合联邦学习中建立线性加速的算法。数值实验验证了理论结果，展示了FedNMap的线性加速性能。
原文摘要 · Abstract (English)
This paper proposes FedNMap, a normal map-based method for composite federated learning, where the objective consists of a smooth loss and a possibly nonsmooth regularizer. FedNMap leverages a normal map-based update scheme to handle the nonsmooth term and incorporates a local correction strategy to mitigate the impact of data heterogeneity across clients. Under standard assumptions, including smooth local losses, weak convexity of the regularizer, and bounded stochastic gradient variance, FedNMap achieves linear speedup with respect to both the number of clients and the number of local updates for nonconvex losses, both with and without the Polyak-Łojasiewicz condition. To the best of our knowledge, this is the first algorithm establishing linear speedup for nonconvex composite federated learning. Numerical experiments corroborate our theoretical findings and demonstrate the linear speedup of FedNMap.
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