# Private Networked Federated Learning for Nonsmooth Objectives

arXiv: https://arxiv.org/abs/2306.14012 · HTML: https://mlsanity.com/paper/2306.14012/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 38 references that are in the map.
- First posted on arXiv 24 Jun 2023.

## Builds on (most cited first, 12 of 12)

- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [Decentralized Federated Learning: Fundamentals, State of the Art, Frameworks, Trends, and Challenges](https://mlsanity.com/paper/2211.08413/) (2022)
- [BrainTorrent: A Peer-to-Peer Environment for Decentralized Federated Learning](https://mlsanity.com/paper/1905.06731/) (2019)
- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [On the Linear Convergence of the ADMM in Decentralized Consensus Optimization](https://mlsanity.com/paper/1307.5561/) (2013)
- [Decentralized Federated Learning via Mutual Knowledge Transfer](https://mlsanity.com/paper/2012.13063/) (2020)
- [DP-ADMM: ADMM-based Distributed Learning with Differential Privacy](https://mlsanity.com/paper/1808.10101/) (2018)
- [Differentially Private Distributed Optimization](https://mlsanity.com/paper/1401.2596/) (2014)
- [Edge Intelligence for Autonomous Driving in 6G Wireless System: Design Challenges and Solutions](https://mlsanity.com/paper/2012.06992/) (2020)
- [Learning Privately over Distributed Features: An ADMM Sharing Approach](https://mlsanity.com/paper/1907.07735/) (2019)
- [The proximal augmented Lagrangian method for nonsmooth composite optimization](https://mlsanity.com/paper/1610.04514/) (2016)

## Abstract (arXiv)

This paper develops a networked federated learning algorithm to solve nonsmooth objective functions. To guarantee the confidentiality of the participants with respect to each other and potential eavesdroppers, we use the zero-concentrated differential privacy notion (zCDP). Privacy is achieved by perturbing the outcome of the computation at each client with a variance-decreasing Gaussian noise. ZCDP allows for better accuracy than the conventional (ε, δ)-DP and stronger guarantees than the more recent R'enyi-DP by assuming adversaries aggregate all the exchanged messages. The proposed algorithm relies on the distributed Alternating Direction Method of Multipliers (ADMM) and uses the approximation of the augmented Lagrangian to handle nonsmooth objective functions. The developed private networked federated learning algorithm has a competitive privacy accuracy trade-off and handles nonsmooth and non-strongly convex problems. We provide complete theoretical proof for the privacy guarantees and the algorithm's convergence to the exact solution. We also prove under additional assumptions that the algorithm converges in O(1/n) ADMM iterations. Finally, we observe the performance of the algorithm in a series of numerical simulations.