# A Highly Efficient Algorithm for Solving Exclusive Lasso Problems

arXiv: https://arxiv.org/abs/2306.14196 · HTML: https://mlsanity.com/paper/2306.14196/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2023.

## Built on by (most cited first, 1 of 1)

- [Autoencoding Random Forests](https://mlsanity.com/paper/2505.21441/) (2025)

## Abstract (arXiv)

The exclusive lasso (also known as elitist lasso) regularizer has become popular recently due to its superior performance on intra-group feature selection. Its complex nature poses difficulties for the computation of high-dimensional machine learning models involving such a regularizer. In this paper, we propose a highly efficient dual Newton method based proximal point algorithm (PPDNA) for solving large-scale exclusive lasso models. As important ingredients, we systematically study the proximal mapping of the weighted exclusive lasso regularizer and the corresponding generalized Jacobian. These results also make popular first-order algorithms for solving exclusive lasso models more practical. Extensive numerical results are presented to demonstrate the superior performance of the PPDNA against other popular numerical algorithms for solving the exclusive lasso problems.