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

Efficient Distributed Hessian Free Algorithm for Large-scale Empirical Risk Minimization via Accumulating Sample Strategy