Title: Faster Coordinate Descent via Adaptive Importance Sampling,
Abstract: Coordinate descent methods employ random partial updates of decision
variables in order to solve huge-scale convex optimization problems. In this
work, we introduce new adaptive rules for the random selection of their
updates. By adaptive, we mean that our selection rules are based on the dual
residual or the primal-dual gap estimates and can change at each iteration. We
theoretically characterize the performance of our selection rules and
demonstrate improvements over the state-of-the-art, and extend our theory and
algorithms to general convex objectives. Numerical evidence with hinge-loss
support vector machines and Lasso confirm that the practice follows the theory.