# Decentralized Multitask Learning over Learned Task Graphs

arXiv: https://arxiv.org/abs/2608.26989 · HTML: https://mlsanity.com/paper/2608.26989/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 27 Aug 2026.

## Builds on (most cited first, 21 of 21)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Model-Contrastive Federated Learning](https://mlsanity.com/paper/2103.16257/) (2021)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization](https://mlsanity.com/paper/1404.6264/) (2014)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Decentralized Collaborative Learning of Personalized Models over Networks](https://mlsanity.com/paper/1610.05202/) (2016)
- [Network Lasso: Clustering and Optimization in Large Graphs](https://mlsanity.com/paper/1507.00280/) (2015)
- [Fully Decentralized Joint Learning of Personalized Models and Collaboration Graphs](https://mlsanity.com/paper/1901.08460/) (2019)
- [Multitask learning over graphs: An Approach for Distributed, Streaming Machine Learning](https://mlsanity.com/paper/2001.02112/) (2020)
- [Dif-MAML: Decentralized Multi-Agent Meta-Learning](https://mlsanity.com/paper/2010.02870/) (2020)
- [Multitask Diffusion Adaptation over Networks](https://mlsanity.com/paper/1311.4894/) (2013)
- [Networked Signal and Information Processing](https://mlsanity.com/paper/2210.13767/) (2022)
- [Learning over Multitask Graphs -- Part II: Performance Analysis](https://mlsanity.com/paper/1805.08547/) (2018)
- [Adaptation and learning over networks under subspace constraints -- Part II: Performance Analysis](https://mlsanity.com/paper/1906.12250/) (2019)
- [Distributed Clustering and Learning Over Networks](https://mlsanity.com/paper/1409.6111/) (2014)
- [Marginal Likelihoods for Distributed Parameter Estimation of Gaussian Graphical Models](https://mlsanity.com/paper/1303.4756/) (2013)
- [Distributed Parameter Estimation in Probabilistic Graphical Models](https://mlsanity.com/paper/1406.3070/) (2014)
- [Structured Cooperative Learning with Graphical Model Priors](https://mlsanity.com/paper/2306.09595/) (2023)
- [Multitask Learning with Learned Task Relationships](https://mlsanity.com/paper/2510.10570/) (2025)

## Abstract (arXiv)

This paper investigates decentralized multitask learning over networks when the underlying task relationships are unknown. While existing graph-regularized multitask frameworks typically assume a known structure, practical settings often require learning inter-task dependencies directly from distributed data. We propose a decentralized two-phase strategy that first estimates a generalized graph Laplacian from noisy non-cooperative stochastic gradient iterates, and subsequently exploits the learned graph to enable cooperative multitask diffusion learning. This framework is motivated by a Gaussian Markov random field prior, which gives rise to a decentralized maximum likelihood estimator for the graph Laplacian. The analysis quantifies the Laplacian estimation error and its propagation to the steady-state performance of the multitask diffusion recursion, and introduces a topology sensitivity index to capture the effect of network heterogeneity. Simulation results corroborate the theoretical findings and demonstrate that cooperation enabled by the learned task graph significantly improves performance over non-cooperative learning, while approaching the true-graph baseline when the estimation stepsize is sufficiently small.