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We propose a novel general algorithm LHAC that efficiently uses second-orderinformation to train a class of large-scale l1-regularized problems. Our methodexecutes cheap iterations while achieving fast local convergence rate byexploiting the special structure of a low-rank matrix, constructed viaquasi-Newton approximation of the Hessian of the smooth loss function. A greedyactive-set strategy, based on the largest violations in the dual constraints,is employed to maintain a working set that iteratively estimates the complementof the optimal active set. This allows for smaller size of subproblems andeventually identifies the optimal active set. Empirical comparisons confirmthat LHAC is highly competitive with several recently proposed state-of-the-artspecialized solvers for sparse logistic regression and sparse inversecovariance matrix selection.

Efficiently Using Second Order Information in Large l1 Regularization Problems