# Learning over Multitask Graphs -- Part I: Stability Analysis

arXiv: https://arxiv.org/abs/1805.08535 · HTML: https://mlsanity.com/paper/1805.08535/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2018.

## Built on by (most cited first, 12 of 12)

- [A New Look and Convergence Rate of Federated Multi-Task Learning with Laplacian Regularization](https://mlsanity.com/paper/2102.07148/) (2021)
- [Networked Signal and Information Processing](https://mlsanity.com/paper/2210.13767/) (2022)
- [Quantization for decentralized learning under subspace constraints](https://mlsanity.com/paper/2209.07821/) (2022)
- [Differential error feedback for communication-efficient decentralized learning](https://mlsanity.com/paper/2406.18418/) (2024)
- [Collaborative likelihood-ratio estimation over graphs](https://mlsanity.com/paper/2205.14461/) (2022)
- [Multitask Learning with Learned Task Relationships](https://mlsanity.com/paper/2510.10570/) (2025)
- [Distributed adaptive algorithm based on the asymmetric cost of error functions](https://mlsanity.com/paper/2107.03067/) (2021)
- [Exact Subspace Diffusion for Decentralized Multitask Learning](https://mlsanity.com/paper/2304.07358/) (2023)
- [Asynchronous Message-Passing and Zeroth-Order Optimization Based Distributed Learning with a Use-Case in Resource Allocation in Communication Networks](https://mlsanity.com/paper/2311.04604/) (2023)
- [Joint estimation of smooth graph signals from partial linear measurements](https://mlsanity.com/paper/2505.23240/) (2025)
- [Quantitative Error Feedback for Quantization Noise Reduction of Filtering over Graphs](https://mlsanity.com/paper/2506.01404/) (2025)
- [A non-smooth regularization framework for learning over multitask graphs](https://mlsanity.com/paper/2509.17728/) (2025)

## Abstract (arXiv)

This paper formulates a multitask optimization problem where agents in the network have individual objectives to meet, or individual parameter vectors to estimate, subject to a smoothness condition over the graph. The smoothness condition softens the transition in the tasks among adjacent nodes and allows incorporating information about the graph structure into the solution of the inference problem. A diffusion strategy is devised that responds to streaming data and employs stochastic approximations in place of actual gradient vectors, which are generally unavailable. The approach relies on minimizing a global cost consisting of the aggregate sum of individual costs regularized by a term that promotes smoothness. We show in this Part I of the work, under conditions on the step-size parameter, that the adaptive strategy induces a contraction mapping and leads to small estimation errors on the order of the small step-size. The results in the accompanying Part II will reveal explicitly the influence of the network topology and the regularization strength on the network performance and will provide insights into the design of effective multitask strategies for distributed inference over networks.