In this paper, we consider solving the distributed optimization problem over a multi-agent network under the communication restricted setting. We study a compressed decentralized stochastic gradient method, termed ``compressed exact diffusion with adaptive stepsizes (CEDAS)", and show the method asymptotically achieves comparable convergence rate as centralized SGD for both smooth strongly convex objective functions and smooth nonconvex objective functions under unbiased compression operators. In particular, to our knowledge, CEDAS enjoys so far the shortest transient time (with respect to the graph specifics) for achieving the convergence rate of centralized SGD, which behaves as $\mathcal{O}(nC^3/(1-\lambda_2)^{2})$ under smooth strongly convex objective functions, and $\mathcal{O}(n^3C^6/(1-\lambda_2)^4)$ under smooth nonconvex objective functions, where $(1-\lambda_2)$ denotes the spectral gap of the mixing matrix, and $C>0$ is the compression-related parameter. Numerical experiments further demonstrate the effectiveness of the proposed algorithm.

翻译：在本文中,我们考虑解决在通信限制设置下多试剂网络中分布的优化问题。 我们研究一种压缩分散式随机梯度方法,称为“通过适应级步骤压缩精确扩散 ”, 并显示这种方法在光滑的强烈矩形目标功能下,在集中的 SGD 中,以集中式 SGD 率实现相似的趋同率,在不偏心操作者下,既可以顺利地快速地快速传递目标功能,也可以顺利地平滑地实现非convex 目标功能下的非CGD 。 特别是,据我们所知, CEDAS 迄今在达到中央SGD(以$\mathcal{O}(n{3/3/(1-\lambda_2)%2美元计算)的趋同率方面享有最短的中程时间(在图形规格方面),即达到中央SGDGD(SGD)的相光谱差距(以$=美元计算出,在平坦式组合矩阵目标功能下, $>0.0美元进一步展示了拟议的压式实验室的有效性。