# Follow the bisector: a simple method for multi-objective optimization

arXiv: https://arxiv.org/abs/2007.06937 · HTML: https://mlsanity.com/paper/2007.06937/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jul 2020.

## Built on by (most cited first, 4 of 4)

- [FAMO: Fast Adaptive Multitask Optimization](https://mlsanity.com/paper/2306.03792/) (2023)
- [Leveraging convergence behavior to balance conflicting tasks in multi-task learning](https://mlsanity.com/paper/2204.06698/) (2022)
- [Fast Line Search for Multi-Task Learning](https://mlsanity.com/paper/2110.00874/) (2021)
- [Uniform Loss vs. Specialized Optimization: A Comparative Analysis in Multi-Task Learning](https://mlsanity.com/paper/2505.10347/) (2025)

## Abstract (arXiv)

This study presents a novel Equiangular Direction Method (EDM) to solve a multi-objective optimization problem. We consider optimization problems, where multiple differentiable losses have to be minimized. The presented method computes descent direction in every iteration to guarantee equal relative decrease of objective functions. This descent direction is based on the normalized gradients of the individual losses. Therefore, it is appropriate to solve multi-objective optimization problems with multi-scale losses. We test the proposed method on the imbalanced classification problem and multi-task learning problem, where standard datasets are used. EDM is compared with other methods to solve these problems.