On the Acceleration of L-BFGS with Second-Order Information and Stochastic Batches

07/14/2018

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by   Jie Liu, et al.

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This paper proposes a framework of L-BFGS based on the (approximate) second-order information with stochastic batches, as a novel approach to the finite-sum minimization problems. Different from the classical L-BFGS where stochastic batches lead to instability, we use a smooth estimate for the evaluations of the gradient differences while achieving acceleration by well-scaling the initial Hessians. We provide theoretical analyses for both convex and nonconvex cases. In addition, we demonstrate that within the popular applications of least-square and cross-entropy losses, the algorithm admits a simple implementation in the distributed environment. Numerical experiments support the efficiency of our algorithms.