Distributed majorization-minimization for Laplacian regularized problems

Abstract

We consider the problem of minimizing a block separable convex function &#x0028 possibly nondifferentiable, and including constraints &#x0029 plus Laplacian regularization, a problem that arises in applications including model fitting, regularizing stratified models, and multi-period portfolio optimization. We develop a distributed majorization-minimization method for this general problem, and derive a complete, self-contained, general, and simple proof of convergence. Our method is able to scale to very large problems, and we illustrate our approach on two applications, demonstrating its scalability and accuracy.