Anderson acceleration of coordinate descent
This work provides a practical speed-up for coordinate descent, a method widely used in machine learning, benefiting practitioners dealing with large-scale optimization problems.
This paper proposes an accelerated version of coordinate descent using extrapolation, addressing the practical speed-up challenges of existing inertial methods. The new approach demonstrates considerable speed-up compared to inertial accelerated coordinate descent and extrapolated (proximal) gradient descent across various machine learning problems.
Acceleration of first order methods is mainly obtained via inertial techniques à la Nesterov, or via nonlinear extrapolation. The latter has known a recent surge of interest, with successful applications to gradient and proximal gradient techniques. On multiple Machine Learning problems, coordinate descent achieves performance significantly superior to full-gradient methods. Speeding up coordinate descent in practice is not easy: inertially accelerated versions of coordinate descent are theoretically accelerated, but might not always lead to practical speed-ups. We propose an accelerated version of coordinate descent using extrapolation, showing considerable speed up in practice, compared to inertial accelerated coordinate descent and extrapolated (proximal) gradient descent. Experiments on least squares, Lasso, elastic net and logistic regression validate the approach.