In recent years, designing distributed optimization algorithms for empirical risk minimization (ERM) has become an active research topic, mainly because of the practical need to deal with the huge volume of data. In this paper, we propose a general framework for training an ERM model by solving its dual problem in parallel over multiple machines. Viewed as special cases of our framework, several existing methods can be better understood. Our method provides a versatile approach for many large-scale machine learning problems, including linear binary multi- class classification, regression, and structured prediction. We show that our method, compared with existing approaches, enjoys global linear convergence for a broader class of problems and achieves faster empirical performance.
We present and study a distributed optimization algorithm by employing a stochastic dual coordinate ascent method. Stochastic dual coordinate ascent methods enjoy strong theoretical guarantees and often have better performances than stochastic gradient descent methods in optimizing regularized loss minimization problems. It still lacks of efforts in studying them in a distributed framework. We make a progress along the line by presenting a distributed stochastic dual coordinate ascent algorithm in a star network, with an analysis of the tradeoff between computation and communication. We verify our analysis by experiments on real data sets. Moreover, we compare the proposed algorithm with distributed stochastic gradient descent methods and distributed alternating direction methods of multipliers for optimizing SVMs in the same distributed framework, and observe competitive performances.