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A polynomial expansion line search for large-scale unconstrained minimization of smooth <i>L</i><sub>2</sub>-regularized loss functions, with implementation in Apache Spark

A polynomial expansion line search for large-scale unconstrained minimization of smooth <i>L</i><sub>2</sub>-regularized loss functions, with implementation in Apache Spark

In large-scale unconstrained optimization algorithms such as limited memory BFGS (LBFGS), a common sub-problem is a line search minimizing the loss function along a descent direction. Commonly used line searches iteratively find an approximate solution for which the Wolfe conditions are satisfied, typically requiring multiple function and gradient evaluations per …