# Safe Peeling for L0-Regularized Least-Squares with supplementary material

arXiv: https://arxiv.org/abs/2302.14471 · HTML: https://mlsanity.com/paper/2302.14471/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 19 references that are in the map.
- First posted on arXiv 28 Feb 2023.

## Builds on (most cited first, 6 of 6)

- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [Best Subset Selection via a Modern Optimization Lens](https://mlsanity.com/paper/1507.03133/) (2015)
- [Fast Best Subset Selection: Coordinate Descent and Local Combinatorial Optimization Algorithms](https://mlsanity.com/paper/1803.01454/) (2018)
- [Sparse Regression at Scale: Branch-and-Bound rooted in First-Order Optimization](https://mlsanity.com/paper/2004.06152/) (2020)
- [A unified approach to mixed-integer optimization problems with logical constraints](https://mlsanity.com/paper/1907.02109/) (2019)
- [Extended Comparisons of Best Subset Selection, Forward Stepwise Selection, and the Lasso](https://mlsanity.com/paper/1707.08692/) (2017)

## Abstract (arXiv)

We introduce a new methodology dubbed ``safe peeling'' to accelerate the resolution of L0-regularized least-squares problems via a Branch-and-Bound (BnB) algorithm. Our procedure enables to tighten the convex relaxation considered at each node of the BnB decision tree and therefore potentially allows for more aggressive pruning. Numerical simulations show that our proposed methodology leads to significant gains in terms of number of nodes explored and overall solving time.s show that our proposed methodology leads to significant gains in terms of number of nodes explored and overall solving time.