Decentralized optimization methods enable on-device training of machine learning models without a central coordinator. In many scenarios communication between devices is energy demanding and time consuming and forms the bottleneck of the entire system. We propose a new randomized first-order method which tackles the communication bottleneck by applying randomized compression operators to the communicated messages. By combining our scheme with a new variance reduction technique that progressively throughout the iterations reduces the adverse effect of the injected quantization noise, we obtain the first scheme that converges linearly on strongly convex decentralized problems while using compressed communication only. We prove that our method can solve the problems without any increase in the number of communications compared to the baseline which does not perform any communication compression while still allowing for a significant compression factor which depends on the conditioning of the problem and the topology of the network. Our key theoretical findings are supported by numerical experiments.

提出了一种新的基于随机压缩算子的一阶随机算法和方差约简技术，能够在去除了通信中数据量的一定压缩的前提下，快速地在分散的装置上完成模型的机器学习训练并收敛于最优解。

分布式优化的线性收敛算法：免费发送更少的比特！