A simple and efficient algorithm for fused lasso signal approximator with convex loss function

TL;DR

This paper introduces a simple, efficient augmented Lagrangian algorithm for the fused lasso signal approximator that handles general convex loss functions, offering ease of implementation and convergence guarantees.

Contribution

The paper presents a novel ALM-based algorithm for FLSA with convex loss, emphasizing simplicity and applicability to various loss functions.

Findings

Algorithm is easy to implement compared to existing methods.

Convergence of the algorithm is established.

Effective on simulation datasets.

Abstract

We consider the augmented Lagrangian method (ALM) as a solver for the fused lasso signal approximator (FLSA) problem. The ALM is a dual method in which squares of the constraint functions are added as penalties to the Lagrangian. In order to apply this method to FLSA, two types of auxiliary variables are introduced to transform the original unconstrained minimization problem into a linearly constrained minimization problem. Each updating in this iterative algorithm consists of just a simple one-dimensional convex programming problem, with closed form solution in many cases. While the existing literature mostly focused on the quadratic loss function, our algorithm can be easily implemented for general convex loss. The most attractive feature of this algorithm is its simplicity in implementation compared to other existing fast solvers. We also provide some convergence analysis of the algorithm. Finally, the method is illustrated with some simulation datasets.