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

TL;DR

This paper presents 'safe peeling', a new method to speed up solving L0-regularized least-squares problems using Branch-and-Bound by tightening relaxations and pruning more efficiently.

Contribution

The paper introduces 'safe peeling', a novel technique that enhances BnB algorithms for L0-regularized problems by improving relaxation tightness and pruning efficiency.

Findings

Significant reduction in nodes explored during BnB

Decreased overall solving time

Improved computational efficiency in sparse regression

Abstract

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.