# Multi-Task Learning as Multi-Objective Optimization

arXiv: https://arxiv.org/abs/1810.04650 · HTML: https://mlsanity.com/paper/1810.04650/

## Key facts

- Cited by 821 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2018.

## Built on by (most cited first, 30 of 821)

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- [Reset-Free Reinforcement Learning via Multi-Task Learning: Learning Dexterous Manipulation Behaviors without Human Intervention](https://mlsanity.com/paper/2104.11203/) (2021)
- [UniverSeg: Universal Medical Image Segmentation](https://mlsanity.com/paper/2304.06131/) (2023)
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- [Multi-Objective Bayesian Optimization over High-Dimensional Search Spaces](https://mlsanity.com/paper/2109.10964/) (2021)
- [Multi-Objective Loss Balancing for Physics-Informed Deep Learning](https://mlsanity.com/paper/2110.09813/) (2021)
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## Abstract (arXiv)

In multi-task learning, multiple tasks are solved jointly, sharing inductive bias between them. Multi-task learning is inherently a multi-objective problem because different tasks may conflict, necessitating a trade-off. A common compromise is to optimize a proxy objective that minimizes a weighted linear combination of per-task losses. However, this workaround is only valid when the tasks do not compete, which is rarely the case. In this paper, we explicitly cast multi-task learning as multi-objective optimization, with the overall objective of finding a Pareto optimal solution. To this end, we use algorithms developed in the gradient-based multi-objective optimization literature. These algorithms are not directly applicable to large-scale learning problems since they scale poorly with the dimensionality of the gradients and the number of tasks. We therefore propose an upper bound for the multi-objective loss and show that it can be optimized efficiently. We further prove that optimizing this upper bound yields a Pareto optimal solution under realistic assumptions. We apply our method to a variety of multi-task deep learning problems including digit classification, scene understanding (joint semantic segmentation, instance segmentation, and depth estimation), and multi-label classification. Our method produces higher-performing models than recent multi-task learning formulations or per-task training.