We consider a distributed learning problem, where agents minimize a global
objective function by exchanging information over a network. Our approach has
two distinct features: (i) It substantially reduces communication by triggering
communication only when necessary, and (ii) it is agnostic to the
data-distribution among the different agents. We can therefore guarantee
convergence even if the local data-distributions of the agents are arbitrarily
distinct. We analyze the convergence rate of the algorithm and derive
accelerated convergence rates in a convex setting. We also characterize the
effect of communication drops and demonstrate that our algorithm is robust to
communication failures. The article concludes by presenting numerical results
from a distributed LASSO problem, and distributed learning tasks on MNIST and
CIFAR-10 datasets. The experiments underline communication savings of 50% or
more due to the event-based communication strategy, show resilience towards
heterogeneous data-distributions, and highlight that our approach outperforms
common baselines such as FedAvg, FedProx, and FedADMM.

分布式学习问题中，通过在网络上交换信息，代理可以最小化全局目标函数。我们的方法具有两个显著特点：只在必要时触发通信以大幅减少通信量，并且对于不同代理的本地数据分布置之不理。我们分析了算法的收敛速度并在凸设置中导出了加速收敛速率。我们还表征了通信丢失的影响，证明了我们的算法对通信故障具有鲁棒性。文章最后提供了分布式 LASSO 问题、MNIST 数据集和 CIFAR-10 数据集上的分布式学习任务的数值结果。实验结果强调了基于事件的通信策略带来的 50% 或更多的通信节省，展示出对异构数据分布的韧性，并凸显我们的方法优于 FedAvg、FedProx 和 FedADMM 等基线方法。