A Fast Alternating Direction Method of Multipliers Algorithm for Big Data Applications

In recent years, with the explosive growth of the data, a wide range of data in Cyber-Physical-Social Systems (CPSS) are generated and collected as big data. Cloud computing have been widely-used as the supporting computation infrastructure, which makes big data analysis gaining much attention from IT industry and academia. Moreover, the data often are distributed and stored in different computation resources in many big data applications. Therefore, distributed computing and optimization has been developed for solving big data problems in cloud computing. time efficiency is the significant bottleneck in the performance of distributed optimization algorithms. In this paper, we propose a novel fast distributed algorithm via Alternating Direction Method of Multipliers with Adaptive Local Update (ADMM-ALU), that uses an efficient adaptive local update strategy to accelerate the speed of convergence by automatically determining the number of inner iterations of local update in each outer iteration (communication round). In particular, our method applies the optimality conditions and the magnitudes of residuals of ADMM to freely steer the trade-off between communication and local computation. Empirically, the performance of our method is tested on several benchmark datasets, and the experimental results show that compared to various versions of ADMM algorithms, our method converges faster, and could be a highly effective and efficient algorithm for practical use in big data applications.