This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines compute gradients of a known empirical loss function using their own local data, and a master machine solves a related minimization problem to update the current estimate. We prove that for nonconvex nonsmooth problems, the proposed algorithm converges to a stationary point with a sublinear rate over the number of communication rounds, coinciding with the best theoretical rate that can be achieved for this class of problems. Linear convergence to a global minimum is established without any statistical assumptions on the local data for problems characterized by composite loss functions whose smooth part is strongly convex. Extensive numerical experiments verify that the performance of the proposed approach indeed improves – sometimes significantly – over other state-of-the-art algorithms in terms of total communication efficiency.

中文翻译：

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凸和非凸问题的一种可证明通信有效的异步分布式推理方法

本文针对异步协议下的一般非凸非平滑信号处理和机器学习问题，提出并分析了一种通信高效的分布式优化框架。在每次迭代中，工作机器使用自己的本地数据计算已知经验损失函数的梯度，并且主机解决相关的最小化问题以更新当前估计。我们证明，对于非凸非光滑问题，所提出的算法在通信轮数上以次线性速率收敛到驻点，与此类问题可以达到的最佳理论速率一致。对于以复合损失函数为特征的问题，其平滑部分是强凸的，在没有对局部数据进行任何统计假设的情况下，建立了到全局最小值的线性收敛。大量的数值实验证实，在总通信效率方面，所提出的方法的性能确实比其他最先进的算法提高了——有时是显着的。