# Smoothing ADMM for Non-convex and Non-smooth Hierarchical Federated Learning

arXiv: https://arxiv.org/abs/2503.08869 · HTML: https://mlsanity.com/paper/2503.08869/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Builds on (most cited first, 20 of 20)

- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [FedMD: Heterogenous Federated Learning via Model Distillation](https://mlsanity.com/paper/1910.03581/) (2019)
- [Client Selection for Federated Learning with Heterogeneous Resources in Mobile Edge](https://mlsanity.com/paper/1804.08333/) (2018)
- [HeteroFL: Computation and Communication Efficient Federated Learning for Heterogeneous Clients](https://mlsanity.com/paper/2010.01264/) (2020)
- [Federated Multi-Task Learning under a Mixture of Distributions](https://mlsanity.com/paper/2108.10252/) (2021)
- [Federated Learning with Label Distribution Skew via Logits Calibration](https://mlsanity.com/paper/2209.00189/) (2022)
- [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)
- [Hierarchical Federated Learning with Quantization: Convergence Analysis and System Design](https://mlsanity.com/paper/2103.14272/) (2021)
- [FedBalancer: Data and Pace Control for Efficient Federated Learning on Heterogeneous Clients](https://mlsanity.com/paper/2201.01601/) (2022)
- [Subgradient methods for sharp weakly convex functions](https://mlsanity.com/paper/1803.02461/) (2018)
- [Douglas-Rachford splitting and ADMM for nonconvex optimization: tight convergence results](https://mlsanity.com/paper/1709.05747/) (2017)
- [Clustered Federated Learning via Generalized Total Variation Minimization](https://mlsanity.com/paper/2105.12769/) (2021)
- [Clustered Federated Learning based on Nonconvex Pairwise Fusion](https://mlsanity.com/paper/2211.04218/) (2022)
- [Smoothing ADMM for Sparse-Penalized Quantile Regression with Non-Convex Penalties](https://mlsanity.com/paper/2309.03094/) (2023)
- [Hierarchical Federated ADMM](https://mlsanity.com/paper/2409.18796/) (2024)
- [Decentralized Smoothing ADMM for Quantile Regression with Non-Convex Sparse Penalties](https://mlsanity.com/paper/2408.01307/) (2024)

## Abstract (arXiv)

This paper presents a hierarchical federated learning (FL) framework that extends the alternating direction method of multipliers (ADMM) with smoothing techniques, tailored for non-convex and non-smooth objectives. Unlike traditional hierarchical FL methods, our approach supports asynchronous updates and multiple updates per iteration, enhancing adaptability to heterogeneous data and system settings. Additionally, we introduce a flexible mechanism to leverage diverse regularization functions at each layer, allowing customization to the specific prior information within each cluster and accommodating (possibly) non-smooth penalty objectives. Depending on the learning goal, the framework supports both consensus and personalization: the total variation norm can be used to enforce consensus across layers, while non-convex penalties such as minimax concave penalty (MCP) or smoothly clipped absolute deviation (SCAD) enable personalized learning. Experimental results demonstrate the superior convergence rates and accuracy of our method compared to conventional approaches, underscoring its robustness and versatility for a wide range of FL scenarios.