In this paper, we propose a Distributed Accumulated Newton Conjugate gradiEnt (DANCE) method in which sample size is gradually increasing to quickly obtain a solution whose empirical loss is under satisfactory statistical accuracy. Our proposed method is multistage in which the solution of a stage serves as a warm start for the next stage which contains more samples (including the samples in the previous stage). The proposed multistage algorithm reduces the number of passes over data to achieve the statistical accuracy of the full training set. Moreover, our algorithm in nature is easy to be distributed and shares the strong scaling property indicating that acceleration is always expected by using more computing nodes. Various iteration complexity results regarding descent direction computation, communication efficiency and stopping criteria are analyzed under convex setting. Our numerical results illustrate that the proposed method outperforms other comparable methods for solving learning problems including neural networks.

In this paper, we study inexact damped Newton method implemented in a distributed environment. We are motivated by the original DiSCO algorithm [Communication-Efficient Distributed Optimization of Self-Concordant Empirical Loss, Yuchen Zhang and Lin Xiao, 2015].We show that this algorithm may not scale well and propose algorithmic modifications which lead to fewer communications and better load-balancing between nodes. Those modifications lead to a more efficient algorithm with better scaling. This was made possibly by introducing our new pre-conditioner which is specially designed so that the preconditioning step can be solved exactly and efficiently.Numerical experiments for minimization of regularized empirical loss with a 273GB instance shows the efficiency of proposed algorithm.

In this paper we generalize the framework of the feasible descent method (FDM) to a randomized (R-FDM) and a coordinate-wise random feasible descent method (RC-FDM) framework. We show that the famous SDCA algorithm for optimizing the SVM dual problem, or the stochastic coordinate descent method for the LASSO problem, fits into the framework of RC-FDM. We prove linear convergence for both R-FDM and RC-FDM under the weak strong convexity assumption. Moreover, we show that the duality gap converges linearly for RC-FDM, which implies that the duality gap also converges linearly for SDCA applied to the SVM dual problem.