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.

我们提出了一种新算法来解决复合联合学习问题，该算法通过策略性地分离近端算子和通信来管理非光滑正则化，并且在没有关于数据相似性的任何假设的情况下解决客户端漂移。此外，每个工作者使用局部更新来降低与服务器的通信频率，并每次通信轮传输仅一个 d 维向量。我们证明了我们的算法线性收敛到最优解的邻域，并在数值实验中展示了我们算法相对于最先进的方法的优越性。

复合异构数据联邦学习

Composite federated learning with heterogeneous data

Mini-batch stochastic gradient descent (SGD) is state of the art in large
scale distributed training. The scheme can reach a linear speedup with respect
to the number of workers, but this is rarely seen in practice as the scheme
often suffers from large network delays and bandwidth limits. To overcome this
communication bottleneck recent works propose to reduce the communication
frequency. An algorithm of this type is local SGD that runs SGD independently
in parallel on different workers and averages the sequences only once in a
while.
This scheme shows promising results in practice, but eluded thorough
theoretical analysis. We prove concise convergence rates for local SGD on
convex problems and show that it converges at the same rate as mini-batch SGD
in terms of number of evaluated gradients, that is, the scheme achieves linear
speedup in the number of workers and mini-batch size. The number of
communication rounds can be reduced up to a factor of T^{1/2}---where T denotes
the number of total steps---compared to mini-batch SGD. This also holds for
asynchronous implementations. Local SGD can also be used for large scale
training of deep learning models.
The results shown here aim serving as a guideline to further explore the
theoretical and practical aspects of local SGD in these applications.

本论文证明了局部随机梯度下降算法在凸问题上能够以与小批量随机梯度下降算法相同的速率收敛，并且与工人数量和小批量大小呈线性加速关系，其中通信轮数可以减少长达 T ^ {1/2} 个因子。