# L1-Regularized Distributed Optimization: A Communication-Efficient Primal-Dual Framework

arXiv: https://arxiv.org/abs/1512.04011 · HTML: https://mlsanity.com/paper/1512.04011/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2015.

## Built on by (most cited first, 4 of 4)

- [Scalable Dual Coordinate Descent for Kernel Methods](https://mlsanity.com/paper/2406.18001/) (2024)
- [Optimizing the Optimal Weighted Average: Efficient Distributed Sparse Classification](https://mlsanity.com/paper/2406.01753/) (2024)
- [On the Relationship Between CoCoA and ADMM for Distributed Empirical Risk Minimization](https://mlsanity.com/paper/2502.00470/) (2025)
- [Simpler Methods Work Better for L1 Penalized Logistic Models and Large Datasets](https://mlsanity.com/paper/2609.23995/) (2026)

## Abstract (arXiv)

Despite the importance of sparsity in many large-scale applications, there are few methods for distributed optimization of sparsity-inducing objectives. In this paper, we present a communication-efficient framework for L1-regularized optimization in the distributed environment. By viewing classical objectives in a more general primal-dual setting, we develop a new class of methods that can be efficiently distributed and applied to common sparsity-inducing models, such as Lasso, sparse logistic regression, and elastic net-regularized problems. We provide theoretical convergence guarantees for our framework, and demonstrate its efficiency and flexibility with a thorough experimental comparison on Amazon EC2. Our proposed framework yields speedups of up to 50x as compared to current state-of-the-art methods for distributed L1-regularized optimization.