# Multi-Task Learning as a Bargaining Game

arXiv: https://arxiv.org/abs/2202.01017 · HTML: https://mlsanity.com/paper/2202.01017/

## Key facts

- Cited by 215 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 65 references that are in the map.
- First posted on arXiv 2 Feb 2022.

## Builds on (most cited first, 30 of 38)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [End-to-End Multi-Task Learning with Attention](https://mlsanity.com/paper/1803.10704/) (2018)
- [Cross-stitch Networks for Multi-task Learning](https://mlsanity.com/paper/1604.03539/) (2016)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Which Tasks Should Be Learned Together in Multi-task Learning?](https://mlsanity.com/paper/1905.07553/) (2019)
- [Multi-Task Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2009.09796/) (2020)
- [Order Matters: Sequence to sequence for sets](https://mlsanity.com/paper/1511.06391/) (2015)
- [Just Pick a Sign: Optimizing Deep Multitask Models with Gradient Sign Dropout](https://mlsanity.com/paper/2010.06808/) (2020)
- [Multi-Task Reinforcement Learning with Context-based Representations](https://mlsanity.com/paper/2102.06177/) (2021)
- [Gradient Vaccine: Investigating and Improving Multi-task Optimization in Massively Multilingual Models](https://mlsanity.com/paper/2010.05874/) (2020)
- [Attentive Single-Tasking of Multiple Tasks](https://mlsanity.com/paper/1904.08918/) (2019)
- [Multi-Task Reinforcement Learning with Soft Modularization](https://mlsanity.com/paper/2003.13661/) (2020)
- [Learning the Pareto Front with Hypernetworks](https://mlsanity.com/paper/2010.04104/) (2020)
- [Instance-aware Semantic Segmentation via Multi-task Network Cascades](https://mlsanity.com/paper/1512.04412/) (2015)
- [Adapting Auxiliary Losses Using Gradient Similarity](https://mlsanity.com/paper/1812.02224/) (2018)
- [Self-Supervised Learning for Domain Adaptation on Point-Clouds](https://mlsanity.com/paper/2003.12641/) (2020)
- [Self-Supervised Generalisation with Meta Auxiliary Learning](https://mlsanity.com/paper/1901.08933/) (2019)
- [A Joint Many-Task Model: Growing a Neural Network for Multiple NLP Tasks](https://mlsanity.com/paper/1611.01587/) (2016)

## Built on by (most cited first, 30 of 215)

- [Twin-Merging: Dynamic Integration of Modular Expertise in Model Merging](https://mlsanity.com/paper/2406.15479/) (2024)
- [Representation Surgery for Multi-Task Model Merging](https://mlsanity.com/paper/2402.02705/) (2024)
- [FAMO: Fast Adaptive Multitask Optimization](https://mlsanity.com/paper/2306.03792/) (2023)
- [Auto-Lambda: Disentangling Dynamic Task Relationships](https://mlsanity.com/paper/2202.03091/) (2022)
- [Independent Component Alignment for Multi-Task Learning](https://mlsanity.com/paper/2305.19000/) (2023)
- [FedDisco: Federated Learning with Discrepancy-Aware Collaboration](https://mlsanity.com/paper/2305.19229/) (2023)
- [Smooth Tchebycheff Scalarization for Multi-Objective Optimization](https://mlsanity.com/paper/2402.19078/) (2024)
- [Revisiting Scalarization in Multi-Task Learning: A Theoretical Perspective](https://mlsanity.com/paper/2308.13985/) (2023)
- [ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks](https://mlsanity.com/paper/2408.11104/) (2024)
- [FAME-ViL: Multi-Tasking Vision-Language Model for Heterogeneous Fashion Tasks](https://mlsanity.com/paper/2303.02483/) (2023)
- [Multimodal Instruction Tuning with Conditional Mixture of LoRA](https://mlsanity.com/paper/2402.15896/) (2024)
- [Fair Resource Allocation in Multi-Task Learning](https://mlsanity.com/paper/2402.15638/) (2024)
- [Direction-oriented Multi-objective Learning: Simple and Provable Stochastic Algorithms](https://mlsanity.com/paper/2305.18409/) (2023)
- [Addressing Negative Transfer in Diffusion Models](https://mlsanity.com/paper/2306.00354/) (2023)
- [Pareto Manifold Learning: Tackling multiple tasks via ensembles of single-task models](https://mlsanity.com/paper/2210.09759/) (2022)
- [ForkMerge: Mitigating Negative Transfer in Auxiliary-Task Learning](https://mlsanity.com/paper/2301.12618/) (2023)
- [Denoising Task Routing for Diffusion Models](https://mlsanity.com/paper/2310.07138/) (2023)
- [Dual-Balancing for Multi-Task Learning](https://mlsanity.com/paper/2308.12029/) (2023)
- [Robust Multi-Task Learning with Excess Risks](https://mlsanity.com/paper/2402.02009/) (2024)
- [CAT Merging: A Training-Free Approach for Resolving Conflicts in Model Merging](https://mlsanity.com/paper/2505.06977/) (2025)
- [HarmonyDream: Task Harmonization Inside World Models](https://mlsanity.com/paper/2310.00344/) (2023)
- [Trust Region-Based Safe Distributional Reinforcement Learning for Multiple Constraints](https://mlsanity.com/paper/2301.10923/) (2023)
- [E2E-MFD: Towards End-to-End Synchronous Multimodal Fusion Detection](https://mlsanity.com/paper/2403.09323/) (2024)
- [Dual Cone Gradient Descent for Training Physics-Informed Neural Networks](https://mlsanity.com/paper/2409.18426/) (2024)
- [Are NeRFs ready for autonomous driving? Towards closing the real-to-simulation gap](https://mlsanity.com/paper/2403.16092/) (2024)
- [Jacobian Descent for Multi-Objective Optimization](https://mlsanity.com/paper/2406.16232/) (2024)
- [Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyond](https://mlsanity.com/paper/2501.10945/) (2025)
- [MUNBa: Machine Unlearning via Nash Bargaining](https://mlsanity.com/paper/2411.15537/) (2024)
- [Selective Task Group Updates for Multi-Task Optimization](https://mlsanity.com/paper/2502.11986/) (2025)
- [Few for Many: Tchebycheff Set Scalarization for Many-Objective Optimization](https://mlsanity.com/paper/2405.19650/) (2024)

## Abstract (arXiv)

In Multi-task learning (MTL), a joint model is trained to simultaneously make predictions for several tasks. Joint training reduces computation costs and improves data efficiency; however, since the gradients of these different tasks may conflict, training a joint model for MTL often yields lower performance than its corresponding single-task counterparts. A common method for alleviating this issue is to combine per-task gradients into a joint update direction using a particular heuristic. In this paper, we propose viewing the gradients combination step as a bargaining game, where tasks negotiate to reach an agreement on a joint direction of parameter update. Under certain assumptions, the bargaining problem has a unique solution, known as the Nash Bargaining Solution, which we propose to use as a principled approach to multi-task learning. We describe a new MTL optimization procedure, Nash-MTL, and derive theoretical guarantees for its convergence. Empirically, we show that Nash-MTL achieves state-of-the-art results on multiple MTL benchmarks in various domains.