# Multitask Diffusion Adaptation over Networks

arXiv: https://arxiv.org/abs/1311.4894 · HTML: https://mlsanity.com/paper/1311.4894/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2013.

## Built on by (most cited first, 11 of 11)

- [Quantization for decentralized learning under subspace constraints](https://mlsanity.com/paper/2209.07821/) (2022)
- [Personalized Graph Federated Learning with Differential Privacy](https://mlsanity.com/paper/2306.06399/) (2023)
- [Decentralized Multi-Task Stochastic Optimization With Compressed Communications](https://mlsanity.com/paper/2112.12373/) (2021)
- [Continual Learning with Distributed Optimization: Does CoCoA Forget?](https://mlsanity.com/paper/2211.16994/) (2022)
- [Multitask Learning with Learned Task Relationships](https://mlsanity.com/paper/2510.10570/) (2025)
- [Design and Analysis of Robust Resilient Diffusion over Multi-Task Networks Against Byzantine Attacks](https://mlsanity.com/paper/2206.12749/) (2022)
- [Robust Non-parametric Knowledge-based Diffusion Least Mean Squares over Adaptive Networks](https://mlsanity.com/paper/2312.01299/) (2023)
- [Distributed Continual Learning with CoCoA in High-dimensional Linear Regression](https://mlsanity.com/paper/2312.01795/) (2023)
- [Low-Communication Resilient Distributed Estimation Algorithm Based on Memory Mechanism](https://mlsanity.com/paper/2508.02705/) (2025)
- [A non-smooth regularization framework for learning over multitask graphs](https://mlsanity.com/paper/2509.17728/) (2025)
- [Decentralized Multitask Learning over Learned Task Graphs](https://mlsanity.com/paper/2608.26989/) (2026)

## Abstract (arXiv)

Adaptive networks are suitable for decentralized inference tasks, e.g., to monitor complex natural phenomena. Recent research works have intensively studied distributed optimization problems in the case where the nodes have to estimate a single optimum parameter vector collaboratively. However, there are many important applications that are multitask-oriented in the sense that there are multiple optimum parameter vectors to be inferred simultaneously, in a collaborative manner, over the area covered by the network. In this paper, we employ diffusion strategies to develop distributed algorithms that address multitask problems by minimizing an appropriate mean-square error criterion with ℓ2-regularization. The stability and convergence of the algorithm in the mean and in the mean-square sense is analyzed. Simulations are conducted to verify the theoretical findings, and to illustrate how the distributed strategy can be used in several useful applications related to spectral sensing, target localization, and hyperspectral data unmixing.