Distributed Majorization-Minimization for Laplacian Regularized Problems

TL;DR

This paper introduces a distributed majorization-minimization algorithm for large-scale Laplacian regularized convex problems, providing convergence guarantees and demonstrating scalability and accuracy in practical applications.

Contribution

It presents a novel distributed optimization method for Laplacian regularized problems with a comprehensive convergence proof and practical scalability.

Findings

Method scales to very large problems.

Demonstrates accuracy in applications.

Provides a complete convergence proof.

Abstract

We consider the problem of minimizing a block separable convex function (possibly nondifferentiable, and including constraints) 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.