# A Fast and Scalable Pathwise-Solver for Group Lasso and Elastic Net Penalized Regression via Block-Coordinate Descent

arXiv: https://arxiv.org/abs/2405.08631 · HTML: https://mlsanity.com/paper/2405.08631/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 42 references that are in the map.
- First posted on arXiv 14 May 2024.

## Builds on (most cited first, 4 of 4)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [sparsegl: An R Package for Estimating Sparse Group Lasso](https://mlsanity.com/paper/2208.02942/) (2022)
- [A Blockwise Descent Algorithm for Group-penalized Multiresponse and Multinomial Regression](https://mlsanity.com/paper/1311.6529/) (2013)
- [The biglasso Package: A Memory- and Computation-Efficient Solver for Lasso Model Fitting with Big Data in R](https://mlsanity.com/paper/1701.05936/) (2017)

## Built on by (most cited first, 5 of 5)

- [LLM-Lasso: A Robust Framework for Domain-Informed Feature Selection and Regularization](https://mlsanity.com/paper/2502.10648/) (2025)
- [Enhanced Cyclic Coordinate Descent Methods for Elastic Net Penalized Linear Models](https://mlsanity.com/paper/2510.19999/) (2025)
- [RandALO: Out-of-sample risk estimation in no time flat](https://mlsanity.com/paper/2409.09781/) (2024)
- [Learning When to Trust LLM Priors: A Validated Framework for Semantic Prior Integration](https://mlsanity.com/paper/2601.21410/) (2026)
- [Interpretable AI with Local Distillation](https://mlsanity.com/paper/2608.23538/) (2026)

## Abstract (arXiv)

We develop fast and scalable algorithms based on block-coordinate descent to solve the group lasso and the group elastic net for generalized linear models along a regularization path. Special attention is given when the loss is the usual least squares loss (Gaussian loss). We show that each block-coordinate update can be solved efficiently using Newton's method and further improved using an adaptive bisection method, solving these updates with a quadratic convergence rate. Our benchmarks show that our package adelie performs 3 to 10 times faster than the next fastest package on a wide array of both simulated and real datasets. Moreover, we demonstrate that our package is a competitive lasso solver as well, matching the performance of the popular lasso package glmnet.