# Efficient Multitask Feature and Relationship Learning

arXiv: https://arxiv.org/abs/1702.04423 · HTML: https://mlsanity.com/paper/1702.04423/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Feb 2017.

## Built on by (most cited first, 7 of 7)

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- [Fair Resource Allocation in Multi-Task Learning](https://mlsanity.com/paper/2402.15638/) (2024)
- [Task-Adaptive Meta-Learning Framework for Advancing Spatial Generalizability](https://mlsanity.com/paper/2212.06864/) (2022)
- [Efficient Network Automatic Relevance Determination](https://mlsanity.com/paper/2506.12352/) (2025)
- [Maneuver Decision-Making For Autonomous Air Combat Through Curriculum Learning And Reinforcement Learning With Sparse Rewards](https://mlsanity.com/paper/2302.05838/) (2023)

## Abstract (arXiv)

We consider a multitask learning problem, in which several predictors are learned jointly. Prior research has shown that learning the relations between tasks, and between the input features, together with the predictor, can lead to better generalization and interpretability, which proved to be useful for applications in many domains. In this paper, we consider a formulation of multitask learning that learns the relationships both between tasks and between features, represented through a task covariance and a feature covariance matrix, respectively. First, we demonstrate that existing methods proposed for this problem present an issue that may lead to ill-posed optimization. We then propose an alternative formulation, as well as an efficient algorithm to optimize it. Using ideas from optimization and graph theory, we propose an efficient coordinate-wise minimization algorithm that has a closed form solution for each block subproblem. Our experiments show that the proposed optimization method is orders of magnitude faster than its competitors. We also provide a nonlinear extension that is able to achieve better generalization than existing methods.