Optimal black-box reductions between optimization objectives

Abstract

The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification task at hand. We reduce the complexity of algorithm design for machine learning by reductions: we develop reductions that take a method developed for one setting and apply it to the entire spectrum of smoothness and strong-convexity in applications. Furthermore, unlike existing results, our new reductions are optimal and more practical. We show how these new reductions give rise to new and faster running times on training linear classifiers for various families of loss functions, and conclude with experiments showing their successes also in practice.