# Monotonic Transformation Invariant Multi-task Learning

arXiv: https://arxiv.org/abs/2509.23948 · HTML: https://mlsanity.com/paper/2509.23948/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 47 references that are in the map.
- First posted on arXiv 28 Sep 2025.

## Builds on (most cited first, 30 of 32)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Meta-World: A Benchmark and Evaluation for Multi-Task and Meta Reinforcement Learning](https://mlsanity.com/paper/1910.10897/) (2019)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [End-to-End Multi-Task Learning with Attention](https://mlsanity.com/paper/1803.10704/) (2018)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [Which Tasks Should Be Learned Together in Multi-task Learning?](https://mlsanity.com/paper/1905.07553/) (2019)
- [Order Matters: Sequence to sequence for sets](https://mlsanity.com/paper/1511.06391/) (2015)
- [Efficiently Identifying Task Groupings for Multi-Task Learning](https://mlsanity.com/paper/2109.04617/) (2021)
- [Multi-Task Learning as a Bargaining Game](https://mlsanity.com/paper/2202.01017/) (2022)
- [Just Pick a Sign: Optimizing Deep Multitask Models with Gradient Sign Dropout](https://mlsanity.com/paper/2010.06808/) (2020)
- [UberNet: Training a `Universal' Convolutional Neural Network for Low-, Mid-, and High-Level Vision using Diverse Datasets and Limited Memory](https://mlsanity.com/paper/1609.02132/) (2016)
- [Qualitatively characterizing neural network optimization problems](https://mlsanity.com/paper/1412.6544/) (2014)
- [Learning to Branch for Multi-Task Learning](https://mlsanity.com/paper/2006.01895/) (2020)
- [Reasonable Effectiveness of Random Weighting: A Litmus Test for Multi-Task Learning](https://mlsanity.com/paper/2111.10603/) (2021)
- [FAMO: Fast Adaptive Multitask Optimization](https://mlsanity.com/paper/2306.03792/) (2023)
- [Do Current Multi-Task Optimization Methods in Deep Learning Even Help?](https://mlsanity.com/paper/2209.11379/) (2022)
- [Revisiting Scalarization in Multi-Task Learning: A Theoretical Perspective](https://mlsanity.com/paper/2308.13985/) (2023)
- [MTL-NAS: Task-Agnostic Neural Architecture Search towards General-Purpose Multi-Task Learning](https://mlsanity.com/paper/2003.14058/) (2020)
- [Fair Resource Allocation in Multi-Task Learning](https://mlsanity.com/paper/2402.15638/) (2024)
- [Loss Functions in the Era of Semantic Segmentation: A Survey and Outlook](https://mlsanity.com/paper/2312.05391/) (2023)
- [Reward Models in Deep Reinforcement Learning: A Survey](https://mlsanity.com/paper/2506.15421/) (2025)
- [GO4Align: Group Optimization for Multi-Task Alignment](https://mlsanity.com/paper/2404.06486/) (2024)
- [Improvable Gap Balancing for Multi-Task Learning](https://mlsanity.com/paper/2307.15429/) (2023)

## Abstract (arXiv)

Multi-task learning (MTL) algorithms typically rely on schemes that combine different task losses or their gradients through weighted averaging. These methods aim to find Pareto stationary points by using heuristics that require access to task loss values, gradients, or both. In doing so, a central challenge arises because task losses can be arbitrarily scaled relative to one another, causing certain tasks to dominate training and degrade overall performance. A recent advance in cooperative bargaining theory, the Direction-based Bargaining Solution (DiBS), yields Pareto stationary solutions immune to task domination because of its invariance to monotonic nonaffine task loss transformations. However, the convergence behavior of DiBS in nonconvex MTL settings is currently not understood. To this end, we prove that under standard assumptions, a subsequence of DiBS iterates converges to a Pareto stationary point when task losses are nonconvex, and propose DiBS-MTL, an adaptation of DiBS to the MTL setting which is more computationally efficient that prior bargaining-inspired MTL approaches. Finally, we empirically show that DiBS-MTL is competitive with leading MTL methods on standard benchmarks, and it drastically outperforms state-of-the-art baselines in multiple examples with poorly-scaled task losses, highlighting the importance of invariance to nonaffine monotonic transformations of the loss landscape. Code available at https://github.com/suryakmurthy/dibs-mtl