# An Iteratively Re-weighted Method for Problems with Sparsity-Inducing Norms

## TL;DR

This paper introduces an iteratively re-weighted algorithm with proven convergence for efficiently solving complex sparsity-inducing norm problems in machine learning, demonstrating superior performance in feature selection tasks.

## Contribution

The paper presents a novel IRW method with convergence guarantees, applicable to various intractable sparsity problems, and validates its effectiveness through real-data experiments.

## Key findings

- IRW method converges reliably and quickly.
- Outperforms alternative optimization methods in feature selection.
- Effective for complex sparsity-inducing norm problems.

## Abstract

This work aims at solving the problems with intractable sparsity-inducing norms that are often encountered in various machine learning tasks, such as multi-task learning, subspace clustering, feature selection, robust principal component analysis, and so on. Specifically, an Iteratively Re-Weighted method (IRW) with solid convergence guarantee is provided. We investigate its convergence speed via numerous experiments on real data. Furthermore, in order to validate the practicality of IRW, we use it to solve a concrete robust feature selection model with complicated objective function. The experimental results show that the model coupled with proposed optimization method outperforms alternative methods significantly.