# Efficient Output Kernel Learning for Multiple Tasks

arXiv: https://arxiv.org/abs/1511.05706 · HTML: https://mlsanity.com/paper/1511.05706/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2015.

## Built on by (most cited first, 9 of 9)

- [On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometry](https://mlsanity.com/paper/2106.00286/) (2021)
- [Variational Multi-Task Learning with Gumbel-Softmax Priors](https://mlsanity.com/paper/2111.05323/) (2021)
- [Riemannian Hamiltonian methods for min-max optimization on manifolds](https://mlsanity.com/paper/2204.11418/) (2022)
- [Entangled Kernels -- Beyond Separability](https://mlsanity.com/paper/2101.05514/) (2021)
- [Task Grouping for Automated Multi-Task Machine Learning via Task Affinity Prediction](https://mlsanity.com/paper/2310.16241/) (2023)
- [Early Recognition of Parkinson's Disease Through Acoustic Analysis and Machine Learning](https://mlsanity.com/paper/2407.16091/) (2024)
- [Robust-Multi-Task Gradient Boosting](https://mlsanity.com/paper/2507.11411/) (2025)
- [Robust multi-task boosting using clustering and local ensembling](https://mlsanity.com/paper/2602.14231/) (2026)
- [Fr'echet Regression on the Bures-Wasserstein Manifold](https://mlsanity.com/paper/2604.03566/) (2026)

## Abstract (arXiv)

The paradigm of multi-task learning is that one can achieve better generalization by learning tasks jointly and thus exploiting the similarity between the tasks rather than learning them independently of each other. While previously the relationship between tasks had to be user-defined in the form of an output kernel, recent approaches jointly learn the tasks and the output kernel. As the output kernel is a positive semidefinite matrix, the resulting optimization problems are not scalable in the number of tasks as an eigendecomposition is required in each step. mboxUsing the theory of positive semidefinite kernels we show in this paper that for a certain class of regularizers on the output kernel, the constraint of being positive semidefinite can be dropped as it is automatically satisfied for the relaxed problem. This leads to an unconstrained dual problem which can be solved efficiently. Experiments on several multi-task and multi-class data sets illustrate the efficacy of our approach in terms of computational efficiency as well as generalization performance.