# Learning over Multitask Graphs -- Part II: Performance Analysis

arXiv: https://arxiv.org/abs/1805.08547 · HTML: https://mlsanity.com/paper/1805.08547/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2018.

## Built on by (most cited first, 6 of 6)

- [A New Look and Convergence Rate of Federated Multi-Task Learning with Laplacian Regularization](https://mlsanity.com/paper/2102.07148/) (2021)
- [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)
- [Quantitative Error Feedback for Quantization Noise Reduction of Filtering over Graphs](https://mlsanity.com/paper/2506.01404/) (2025)
- [Decentralized Multitask Learning over Learned Task Graphs](https://mlsanity.com/paper/2608.26989/) (2026)
- [Data-Topology Compatibility Enables Personalization in Decentralized Learning](https://mlsanity.com/paper/2610.15126/) (2026)

## Abstract (arXiv)

Part I of this paper formulated 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. A diffusion strategy was devised that responds to streaming data and employs stochastic approximations in place of actual gradient vectors, which are generally unavailable. The approach relied on minimizing a global cost consisting of the aggregate sum of individual costs regularized by a term that promotes smoothness. We examined the first-order, the second-order, and the fourth-order stability of the multitask learning algorithm. The results identified conditions on the step-size parameter, regularization strength, and data characteristics in order to ensure stability. This Part II examines steady-state performance of the strategy. The results reveal explicitly the influence of the network topology and the regularization strength on the network performance and provide insights into the design of effective multitask strategies for distributed inference over networks.