Curvature-Exploiting Acceleration of Elastic Net Computations

Abstract: This paper introduces an efficient second-order method for solving the elastic net problem. Its key innovation is a computationally efficient technique for injecting curvature information in the optimization process which admits a strong theoretical performance guarantee. In particular, we show improved run time over popular first-order methods and quantify the speed-up in terms of statistical measures of the data matrix. The improved time complexity is the result of an extensive exploitation of the problem structure and a careful combination of second-order information, variance reduction techniques, and momentum acceleration. Beside theoretical speed-up, experimental results demonstrate great practical performance benefits of curvature information, especially for ill-conditioned data sets.