We propose a novel algorithm for solving the composite Federated Learning (FL) problem. This algorithm manages non-smooth regularization by strategically decoupling the proximal operator and communication, and addresses client drift without any assumptions about data similarity. Moreover, each worker uses local updates to reduce the communication frequency with the server and transmits only a $d$-dimensional vector per communication round. We prove that our algorithm converges linearly to a neighborhood of the optimal solution and demonstrate the superiority of our algorithm over state-of-the-art methods in numerical experiments.

翻译：我们提出了一种解决复合联邦学习（FL）问题的新算法。该算法通过策略性地解耦近端算子与通信过程，有效处理了非光滑正则化项，并在不假设数据相似性的前提下解决了客户端漂移问题。此外，每个工作节点采用本地更新策略以降低与服务器的通信频率，且每轮通信仅传输一个$d$维向量。我们证明了所提算法能以线性速率收敛至最优解的邻域，并通过数值实验验证了该算法相较于现有最优方法的优越性。