How a Small Amount of Data Sharing Benefits Distributed Optimization and Learning

Abstract: While distributed optimization algorithms have the merits in parallel processing and protecting local data security, they often suffer from slow convergence compared with centralized optimization algorithms. This paper focuses on how small amount of data sharing could benefit distributed optimization and learning for more advanced optimization algorithms. Specifically, we consider how data sharing could benefit distributed multi-block alternating direction method of multipliers (ADMM) and preconditioned conjugate gradient method (PCG) with application in machine learning tasks of linear and logistic regression. These algorithms are commonly known as algorithms between the first and the second order methods, and we show that data sharing could hugely boost the convergence speed for this class of the algorithms. Theoretically, we prove that a small amount of data share leads to improvements from near-worst to near-optimal convergence rate when applying ADMM and PCG methods to machine learning tasks. We further propose a meta randomized data-sharing scheme and provide its tailored applications in multi-block ADMM and PCG methods in order to enjoy both the benefit from data-sharing and from the efficiency of distributed computing. From the numerical evidences, we are convinced that our algorithms provide good quality of estimators in both the least square and the logistic regressions within much fewer iterations by only sharing 5% of pre-fixed data, while purely distributed optimization algorithms may take hundreds more times of iterations to converge. We hope that the discovery resulted from this paper would encourage even a small amount of data sharing among different regions to combat difficult global learning problems.

Mathematics Subject Classification ID

Convex programming (90C25) Large-scale problems in mathematical programming (90C06)

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