# One to beat them all: "RYU" -- a unifying framework for the construction of safe balls

arXiv: https://arxiv.org/abs/2312.00640 · HTML: https://mlsanity.com/paper/2312.00640/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 29 references that are in the map.
- First posted on arXiv 1 Dec 2023.

## Builds on (most cited first, 13 of 13)

- [Learning with Fenchel-Young Losses](https://mlsanity.com/paper/1901.02324/) (2019)
- [Gap Safe screening rules for sparsity enforcing penalties](https://mlsanity.com/paper/1611.05780/) (2016)
- [Mind the duality gap: safer rules for the Lasso](https://mlsanity.com/paper/1505.03410/) (2015)
- [A Safe Screening Rule for Sparse Logistic Regression](https://mlsanity.com/paper/1307.4145/) (2013)
- [Safe Screening With Variational Inequalities and Its Application to LASSO](https://mlsanity.com/paper/1307.7577/) (2013)
- [Safe Grid Search with Optimal Complexity](https://mlsanity.com/paper/1810.05471/) (2018)
- [Screening Rules and its Complexity for Active Set Identification](https://mlsanity.com/paper/2009.02709/) (2020)
- [Safe rules for the identification of zeros in the solutions of the SLOPE problem](https://mlsanity.com/paper/2110.11784/) (2021)
- [Safe squeezing for antisparse coding](https://mlsanity.com/paper/1911.07508/) (2019)
- [Dynamic Sasvi: Strong Safe Screening for Norm-Regularized Least Squares](https://mlsanity.com/paper/2102.04108/) (2021)
- [Screen & Relax: Accelerating the resolution of Elastic-net by safe identification of the solution support](https://mlsanity.com/paper/2110.07281/) (2021)
- [Stable safe screening and structured dictionaries for faster L1 regularization](https://mlsanity.com/paper/1812.06635/) (2018)
- [Beyond GAP screening for Lasso by exploiting new dual cutting half-spaces with supplementary material](https://mlsanity.com/paper/2203.00987/) (2022)

## Built on by (most cited first, 2 of 2)

- [El0ps: An Exact L0-regularized Problems Solver](https://mlsanity.com/paper/2506.06373/) (2025)
- [Gap Safe Screening Rules for Fast Training of Robust Support Vector Machines under Feature Noise](https://mlsanity.com/paper/2603.25221/) (2026)

## Abstract (arXiv)

In this paper, we present a new framework, called "RYU" for constructing "safe" regions -- specifically, bounded sets that are guaranteed to contain the dual solution of a target optimization problem. Our framework applies to the standard case where the objective function is composed of two components: a closed, proper, convex function with Lipschitz-smooth gradient and another closed, proper, convex function. We show that the RYU framework not only encompasses but also improves upon the state-of-the-art methods proposed over the past decade for this class of optimization problems.