# Decentralized Smoothing ADMM for Quantile Regression with Non-Convex Sparse Penalties

arXiv: https://arxiv.org/abs/2408.01307 · HTML: https://mlsanity.com/paper/2408.01307/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 35 references that are in the map.
- First posted on arXiv 2 Aug 2024.

## Builds on (most cited first, 6 of 6)

- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Nonconvex Problems](https://mlsanity.com/paper/1410.1390/) (2014)
- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [Douglas-Rachford splitting and ADMM for nonconvex optimization: tight convergence results](https://mlsanity.com/paper/1709.05747/) (2017)
- [Quantile Regression Under Memory Constraint](https://mlsanity.com/paper/1810.08264/) (2018)
- [Smoothing ADMM for Sparse-Penalized Quantile Regression with Non-Convex Penalties](https://mlsanity.com/paper/2309.03094/) (2023)

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

- [Smoothing ADMM for Non-convex and Non-smooth Hierarchical Federated Learning](https://mlsanity.com/paper/2503.08869/) (2025)
- [Federated Smoothing ADMM for Localization](https://mlsanity.com/paper/2503.09497/) (2025)

## Abstract (arXiv)

In the rapidly evolving internet-of-things (IoT) ecosystem, effective data analysis techniques are crucial for handling distributed data generated by sensors. Addressing the limitations of existing methods, such as the sub-gradient approach, which fails to distinguish between active and non-active coefficients effectively, this paper introduces the decentralized smoothing alternating direction method of multipliers (DSAD) for penalized quantile regression. Our method leverages non-convex sparse penalties like the minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD), improving the identification and retention of significant predictors. DSAD incorporates a total variation norm within a smoothing ADMM framework, achieving consensus among distributed nodes and ensuring uniform model performance across disparate data sources. This approach overcomes traditional convergence challenges associated with non-convex penalties in decentralized settings. We present theoretical proofs and extensive simulation results to validate the effectiveness of the DSAD, demonstrating its superiority in achieving reliable convergence and enhancing estimation accuracy compared with prior methods.