Distributed sparse learning with a cluster of multiple machines has attracted much attention in machine learning, especially for large-scale applications with high-dimensional data. One popular way to implement sparse learning is to use L1 regularization. In this paper, we propose a novel method, called proximal SCOPE (pSCOPE), for distributed sparse learning with L1 regularization. pSCOPE is based on a cooperative autonomous local learning (CALL) framework. In the CALL framework of pSCOPE, we find that the data partition affects the convergence of the learning procedure, and subsequently we define a metric to measure the goodness of a data partition. Based on the defined metric, we theoretically prove that pSCOPE is convergent with a linear convergence rate if the data partition is good enough. We also prove that better data partition implies faster convergence rate. Furthermore, pSCOPE is also communication efficient. Experimental results on real data sets show that pSCOPE can outperform other state-of-the-art distributed methods for sparse learning.

Many machine learning models, such as logistic regression (LR) and support vector machine (SVM), can be formulated as composite optimization problems. Recently, many distributed stochastic optimization (DSO) methods have been proposed to solve the large-scale composite optimization problems, which have shown better performance than traditional batch methods. However, most of these DSO methods might not be scalable enough. In this paper, we propose a novel DSO method, called scalable composite optimization for learning (SCOPE), and implement it on the fault-tolerant distributed platform Spark. SCOPE is both computation-efficient and communication-efficient. Theoretical analysis shows that SCOPE is convergent with linear convergence rate when the objective function is strongly convex. Furthermore, empirical results on real datasets show that SCOPE can outperform other state-of-the-art distributed learning methods on Spark, including both batch learning methods and DSO methods.

Stochastic gradient descent (SGD) and its variants have attracted much attention in machine learning due to their efficiency and effectiveness for optimization. To handle large-scale problems, researchers have recently proposed several lock-free strategy based parallel SGD (LF-PSGD) methods for multi-core systems. However, existing works have only proved the convergence of these LF-PSGD methods for convex problems. To the best of our knowledge, no work has proved the convergence of the LF-PSGD methods for non-convex problems. In this paper, we provide the theoretical proof about the convergence of two representative LF-PSGD methods, Hogwild! and AsySVRG, for non-convex problems. Empirical results also show that both Hogwild! and AsySVRG are convergent on non-convex problems, which successfully verifies our theoretical results.

Stochastic gradient descent (SGD) and its variants have become more and more popular in machine learning due to their efficiency and effectiveness. To handle large-scale problems, researchers have recently proposed several parallel SGD methods for multicore systems. However, existing parallel SGD methods cannot achieve satisfactory performance in real applications. In this paper, we propose a fast asynchronous parallel SGD method, called AsySVRG, by designing an asynchronous strategy to parallelize the recently proposed SGD variant called stochastic variance reduced gradient (SVRG). AsySVRG adopts a lock-free strategy which is more efficient than other strategies with locks. Furthermore, we theoretically prove that AsySVRG is convergent with a linear convergence rate. Both theoretical and empirical results show that AsySVRG can outperform existing state-of-the-art parallel SGD methods like Hogwild! in terms of convergence rate and computation cost.