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We consider large scale empirical risk minimization (ERM) problems, whereboth the problem dimension and variable size is large. In these cases, mostsecond order methods are infeasible due to the high cost in both computing theHessian over all samples and computing its inverse in high dimensions. In thispaper, we propose a novel adaptive sample size second-order method, whichreduces the cost of computing the Hessian by solving a sequence of ERM problemscorresponding to a subset of samples and lowers the cost of computing theHessian inverse using a truncated eigenvalue decomposition. We show that whilewe geometrically increase the size of the training set at each stage, a singleiteration of the truncated Newton method is sufficient to solve the new ERMwithin its statistical accuracy. Moreover, for a large number of samples we areallowed to double the size of the training set at each stage, and the proposedmethod subsequently reaches the statistical accuracy of the full training setapproximately after two effective passes. In addition to this theoreticalresult, we show empirically on a number of well known data sets that theproposed truncated adaptive sample size algorithm outperforms stochasticalternatives for solving ERM problems.

Large Scale Empirical Risk Minimization via Truncated Adaptive Newton Method