Stochastic Dual Coordinate Descent with Bandit Sampling

Coordinate descent methods minimize a cost function by updating a single decision variable (corresponding to one coordinate) at a time. Ideally, one would update the decision variable that yields the largest marginal decrease in the cost function. However, finding this coordinate would require checking all of them, which is not computationally practical. We instead propose a new adaptive method for coordinate descent. First, we define a lower bound on the decrease of the cost function when a coordinate is updated and, instead of calculating this lower bound for all coordinates, we use a multi-armed bandit algorithm to learn which coordinates result in the largest marginal decrease while simultaneously performing coordinate descent. We show that our approach improves the convergence of the coordinate methods (including parallel versions) both theoretically and experimentally.