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We propose a fast proximal Newton-type algorithm for minimizing regularized finite sums that returns an ϵ-suboptimal point in Õ(d(n + √(κ d))(1/ϵ)) FLOPS, where n is number of samples, d is feature dimension, and κ is the condition number. As long as n > d, the proposed method is more efficient than state-of-the-art accelerated stochastic first-order methods for non-smooth regularizers which requires Õ(d(n + √(κ n))(1/ϵ)) FLOPS. The key idea is to form the subsampled Newton subproblem in a wayarXiv:1708.08552v1 fatcat:pr7nrwnc3jaybize2k2544ml3i