Asynchronous Distributed ADMM for Large-Scale Optimization- Part II: Linear Convergence Analysis and Numerical Performance
This work addresses the problem of slow convergence in large-scale optimization for machine learning practitioners, but it is incremental as it builds on prior analysis of the same algorithm.
The authors tackled the scalability issue of synchronous distributed ADMM by analyzing conditions for linear convergence in their asynchronous version (AD-ADMM), demonstrating its superior time efficiency on a large-scale logistic regression problem with a 2-3x speedup over synchronous methods.
The alternating direction method of multipliers (ADMM) has been recognized as a versatile approach for solving modern large-scale machine learning and signal processing problems efficiently. When the data size and/or the problem dimension is large, a distributed version of ADMM can be used, which is capable of distributing the computation load and the data set to a network of computing nodes. Unfortunately, a direct synchronous implementation of such algorithm does not scale well with the problem size, as the algorithm speed is limited by the slowest computing nodes. To address this issue, in a companion paper, we have proposed an asynchronous distributed ADMM (AD-ADMM) and studied its worst-case convergence conditions. In this paper, we further the study by characterizing the conditions under which the AD-ADMM achieves linear convergence. Our conditions as well as the resulting linear rates reveal the impact that various algorithm parameters, network delay and network size have on the algorithm performance. To demonstrate the superior time efficiency of the proposed AD-ADMM, we test the AD-ADMM on a high-performance computer cluster by solving a large-scale logistic regression problem.