# A Random Block-Coordinate Douglas-Rachford Splitting Method with Low Computational Complexity for Binary Logistic Regression

arXiv: https://arxiv.org/abs/1712.09131 · HTML: https://mlsanity.com/paper/1712.09131/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Dec 2017.

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

- [A High Dimensional Statistical Model for Adversarial Training: Geometry and Trade-Offs](https://mlsanity.com/paper/2402.05674/) (2024)
- [On the Existence of Consistent Adversarial Attacks in High-Dimensional Linear Classification](https://mlsanity.com/paper/2506.12454/) (2025)

## Abstract (arXiv)

In this paper, we propose a new optimization algorithm for sparse logistic regression based on a stochastic version of the Douglas-Rachford splitting method. Our algorithm sweeps the training set by randomly selecting a mini-batch of data at each iteration, and it allows us to update the variables in a block coordinate manner. Our approach leverages the proximity operator of the logistic loss, which is expressed with the generalized Lambert W function. Experiments carried out on standard datasets demonstrate the efficiency of our approach w.r.t. stochastic gradient-like methods.