Decentralized optimization and communication compression have exhibited their great potential in accelerating distributed machine learning by mitigating the communication bottleneck in practice. While existing decentralized algorithms with communication compression mostly focus on the problems with only smooth components, we study the decentralized stochastic composite optimization problem with a potentially non-smooth component. A \underline{Prox}imal gradient \underline{L}in\underline{EA}r convergent \underline{D}ecentralized algorithm with compression, Prox-LEAD, is proposed with rigorous theoretical analyses in the general stochastic setting and the finite-sum setting. Our theorems indicate that Prox-LEAD works with arbitrary compression precision, and it tremendously reduces the communication cost almost for free. The superiorities of the proposed algorithms are demonstrated through the comparison with state-of-the-art algorithms in terms of convergence complexities and numerical experiments. Our algorithmic framework also generally enlightens the compressed communication on other primal-dual algorithms by reducing the impact of inexact iterations, which might be of independent interest.

翻译：分散化优化和通信压缩在通过减少通信瓶颈来加速分布式机器学习方面展现了巨大的潜力。 虽然现有的分散式通信压缩算法主要侧重于只有光滑组件的问题,但我们研究的是分散式混合优化化问题,其中可能含有非光滑组件。 下线{ Prox-LEA}r 集中式缩压法( Prox- LEAD) 与压缩法( Prox- LEAD) 的集中化算法( Prox- LEAD) 相比, 提出了严格的理论分析。 我们的理论显示, Prox- LEAD 使用任意压缩精度, 并极大地降低了几乎免费的通信成本。 拟议的算法的优越性通过在聚合复杂性和数字实验方面与最先进的算法的比较得到证明。 我们的算法框架还通常通过减少直截现象的影响来引导其他原始算法的压缩式算法( 可能具有独立的兴趣 ) 。