Yao Li

Xiaorui Liu, Yao Li, Rongrong Wang et al.

Communication compression has become a key strategy to speed up distributed optimization. However, existing decentralized algorithms with compression mainly focus on compressing DGD-type algorithms. They are unsatisfactory in terms of convergence rate, stability, and the capability to handle heterogeneous data. Motivated by primal-dual algorithms, this paper proposes the first \underline{L}in\underline{EA}r convergent \underline{D}ecentralized algorithm with compression, LEAD. Our theory describes the coupled dynamics of the inexact primal and dual update as well as compression error, and we provide the first consensus error bound in such settings without assuming bounded gradients. Experiments on convex problems validate our theoretical analysis, and empirical study on deep neural nets shows that LEAD is applicable to non-convex problems.

Yao Li, Ming Yan

Decentralized algorithms solve multi-agent problems over a connected network, where the information can only be exchanged with the accessible neighbors. Though there exist several decentralized optimization algorithms, there are still gaps in convergence conditions and rates between decentralized and centralized algorithms. In this paper, we fill some gaps by considering two decentralized algorithms: EXTRA and NIDS. They both converge linearly with strongly convex objective functions. We will answer two questions regarding them. What are the optimal upper bounds for their stepsizes? Do decentralized algorithms require more properties on the functions for linear convergence than centralized ones? More specifically, we relax the required conditions for linear convergence of both algorithms. For EXTRA, we show that the stepsize is comparable to that of centralized algorithms. For NIDS, the upper bound of the stepsize is shown to be exactly the same as the centralized ones. In addition, we relax the requirement for the objective functions and the mixing matrices. We provide the linear convergence results for both algorithms under the weakest conditions.