HSAC-ALADMM: an asynchronous lazy ADMM algorithm based on hierarchical sparse allreduce communication

Abstract

The distributed alternating direction method of multipliers (ADMM) is an effective algorithm for solving large-scale optimization problems. However, its high communication cost limits its scalability. An asynchronous lazy ADMM algorithm based on hierarchical sparse allreduce communication mode (HSAC-ALADMM) is proposed to reduce the communication cost of the distributed ADMM: firstly, this paper proposes a lazily aggregate parameters strategy to filter the transmission parameters of the distributed ADMM, which reduces the payload of the node per iteration. Secondly, a hierarchical sparse allreduce communication mode is tailored for sparse data to aggregate the filtered transmission parameters effectively. Finally, a Calculator-Communicator-Manager framework is designed to implement the proposed algorithm, which combines the asynchronous communication protocol and the allreduce communication mode effectively. It separates the calculation and communication by multithreading, thus improving the efficiency of system calculation and communication. Experimental results for the L1-regularized logistic regression problem with public datasets show that the HSAC-ALADMM algorithm is faster than existing asynchronous ADMM algorithms. Compared with existing sparse allreduce algorithms, the hierarchical sparse allreduce algorithm proposed in this paper makes better use of the characteristics of sparse data to reduce system time in multi-core cluster.