# Screening Rules and its Complexity for Active Set Identification

arXiv: https://arxiv.org/abs/2009.02709 · HTML: https://mlsanity.com/paper/2009.02709/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2020.

## Built on by (most cited first, 8 of 8)

- [Beyond L1: Faster and Better Sparse Models with skglm](https://mlsanity.com/paper/2204.07826/) (2022)
- [An Accelerated Doubly Stochastic Gradient Method with Faster Explicit Model Identification](https://mlsanity.com/paper/2208.06058/) (2022)
- [Safe rules for the identification of zeros in the solutions of the SLOPE problem](https://mlsanity.com/paper/2110.11784/) (2021)
- [Dynamic Sasvi: Strong Safe Screening for Norm-Regularized Least Squares](https://mlsanity.com/paper/2102.04108/) (2021)
- [Continuation Path with Linear Convergence Rate](https://mlsanity.com/paper/2112.05104/) (2021)
- [One to beat them all: "RYU" -- a unifying framework for the construction of safe balls](https://mlsanity.com/paper/2312.00640/) (2023)
- [A Screening Strategy for Structured Optimization Involving Nonconvex ℓq,p Regularization](https://mlsanity.com/paper/2208.02161/) (2022)
- [El0ps: An Exact L0-regularized Problems Solver](https://mlsanity.com/paper/2506.06373/) (2025)

## Abstract (arXiv)

Screening rules were recently introduced as a technique for explicitly identifying active structures such as sparsity, in optimization problem arising in machine learning. This has led to new methods of acceleration based on a substantial dimension reduction. We show that screening rules stem from a combination of natural properties of subdifferential sets and optimality conditions, and can hence be understood in a unified way. Under mild assumptions, we analyze the number of iterations needed to identify the optimal active set for any converging algorithm. We show that it only depends on its convergence rate.