mlsanityData to 7 Oct 2026

Multi-Task Learning as a Bargaining Game

arXiv 2202.01017 ↗First posted 2 Feb 2022cs.LG cs.GTcited by 209

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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.

Key facts. Cited by 209 papers in the map (data through 7 Oct 2026). Builds on 38 of its 65 references that are in the map. First posted on arXiv 2 Feb 2022.

Builds on

38 of 65 references.

References · 38

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2018Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actorcited by 4,635
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  7. 2017Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semanticscited by 1,345
  8. 2020Gradient Surgery for Multi-Task Learningcited by 1,210
  9. 2019Meta-World: A Benchmark and Evaluation for Multi-Task and Meta Reinforcement Learningcited by 1,168
  10. 2017GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networkscited by 816
  11. 2018Multi-Task Learning as Multi-Objective Optimizationcited by 809
  12. 2017An Overview of Multi-Task Learning in Deep Neural Networkscited by 791
26 more
  1. 2020Directional Message Passing for Molecular Graphscited by 556
  2. 2018End-to-End Multi-Task Learning with Attentioncited by 533
  3. 2016Cross-stitch Networks for Multi-task Learningcited by 466
  4. 2019Provably Powerful Graph Networkscited by 385
  5. 2020Multi-Task Learning with Deep Neural Networks: A Surveycited by 374
  6. 2019Which Tasks Should Be Learned Together in Multi-task Learning?cited by 367
  7. 2015Order Matters: Sequence to sequence for setscited by 236
  8. 2020Just Pick a Sign: Optimizing Deep Multitask Models with Gradient Sign Dropoutcited by 199
  9. 2021Multi-Task Reinforcement Learning with Context-based Representationscited by 169
  10. 2020Gradient Vaccine: Investigating and Improving Multi-task Optimization in Massively Multilingual Modelscited by 167
  11. 2019Attentive Single-Tasking of Multiple Taskscited by 148
  12. 2020Multi-Task Reinforcement Learning with Soft Modularizationcited by 138
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  14. 2015Instance-aware Semantic Segmentation via Multi-task Network Cascadescited by 120
  15. 2020Self-Supervised Learning for Domain Adaptation on Point-Cloudscited by 99
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  17. 2019Self-Supervised Generalisation with Meta Auxiliary Learningcited by 88
  18. 2016A Joint Many-Task Model: Growing a Neural Network for Multiple NLP Taskscited by 62
  19. 2018A Modulation Module for Multi-task Learning with Applications in Image Retrievalcited by 49
  20. 2020Auxiliary Learning by Implicit Differentiationcited by 45
  21. 2019Ray Interference: a Source of Plateaus in Deep Reinforcement Learningcited by 40
  22. 2016Learning to Push by Grasping: Using multiple tasks for effective learningcited by 36
  23. 2019Regularizing Deep Multi-Task Networks using Orthogonal Gradientscited by 36
  24. 2019First-order methods almost always avoid saddle points: the case of vanishing step-sizescited by 35
  25. 2021Fair Exploration via Axiomatic Bargainingcited by 21
  26. 2019The Kalai-Smorodinski solution for many-objective Bayesian optimizationcited by 13

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 5; 2023: 29; 2024: 54; 2025: 60; 2026: 61.

209 papers.

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  1. 2024Twin-Merging: Dynamic Integration of Modular Expertise in Model Mergingcited by 114
  2. 2024Representation Surgery for Multi-Task Model Mergingcited by 95
  3. 2023FAMO: Fast Adaptive Multitask Optimizationcited by 74
  4. 2022Auto-Lambda: Disentangling Dynamic Task Relationshipscited by 73
  5. 2023Independent Component Alignment for Multi-Task Learningcited by 69
  6. 2023FedDisco: Federated Learning with Discrepancy-Aware Collaborationcited by 66
  7. 2023Revisiting Scalarization in Multi-Task Learning: A Theoretical Perspectivecited by 51
  8. 2024Smooth Tchebycheff Scalarization for Multi-Objective Optimizationcited by 50
  9. 2024ConFIG: Towards Conflict-free Training of Physics Informed Neural Networkscited by 43
  10. 2023FAME-ViL: Multi-Tasking Vision-Language Model for Heterogeneous Fashion Taskscited by 37
  11. 2024Multimodal Instruction Tuning with Conditional Mixture of LoRAcited by 36
  12. 2024Fair Resource Allocation in Multi-Task Learningcited by 34
38 more
  1. 2023Direction-oriented Multi-objective Learning: Simple and Provable Stochastic Algorithmscited by 33
  2. 2023Addressing Negative Transfer in Diffusion Modelscited by 33
  3. 2022Pareto Manifold Learning: Tackling multiple tasks via ensembles of single-task modelscited by 29
  4. 2023ForkMerge: Mitigating Negative Transfer in Auxiliary-Task Learningcited by 28
  5. 2023Denoising Task Routing for Diffusion Modelscited by 28
  6. 2023Dual-Balancing for Multi-Task Learningcited by 27
  7. 2024Robust Multi-Task Learning with Excess Riskscited by 23
  8. 2023HarmonyDream: Task Harmonization Inside World Modelscited by 22
  9. 2025CAT Merging: A Training-Free Approach for Resolving Conflicts in Model Mergingcited by 22
  10. 2024E2E-MFD: Towards End-to-End Synchronous Multimodal Fusion Detectioncited by 21
  11. 2024Dual Cone Gradient Descent for Training Physics-Informed Neural Networkscited by 21
  12. 2023Trust Region-Based Safe Distributional Reinforcement Learning for Multiple Constraintscited by 20
  13. 2024Are NeRFs ready for autonomous driving? Towards closing the real-to-simulation gapcited by 20
  14. 2024Jacobian Descent for Multi-Objective Optimizationcited by 18
  15. 2024MUNBa: Machine Unlearning via Nash Bargainingcited by 17
  16. 2022Beyond Losses Reweighting: Empowering Multi-Task Learning via the Generalization Perspectivecited by 15
  17. 2024Few for Many: Tchebycheff Set Scalarization for Many-Objective Optimizationcited by 15
  18. 2025Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyondcited by 15
  19. 2025Selective Task Group Updates for Multi-Task Optimizationcited by 15
  20. 2025SplitFlow: Flow Decomposition for Inversion-Free Text-to-Image Editingcited by 15
  21. 2022Mitigating Gradient Bias in Multi-objective Learning: A Provably Convergent Stochastic Approachcited by 14
  22. 2023Fairness in Multi-Task Learning via Wasserstein Barycenterscited by 14
  23. 2024Pareto Low-Rank Adapters: Efficient Multi-Task Learning with Preferencescited by 13
  24. 2023Auxiliary Learning as an Asymmetric Bargaining Gamecited by 12
  25. 2024Exploring Training on Heterogeneous Data with Mixture of Low-rank Adapterscited by 12
  26. 2024SurgeryV2: Bridging the Gap Between Model Merging and Multi-Task Learning with Deep Representation Surgerycited by 12
  27. 2024Understanding Forgetting in LLM Supervised Fine-Tuning and Preference Learning -- A Convex Optimization Perspectivecited by 12
  28. 2024Proactive Gradient Conflict Mitigation in Multi-Task Learning: A Sparse Training Perspectivecited by 12
  29. 2026DanceOPD: On-Policy Generative Field Distillationcited by 12
  30. 2024Bayesian Uncertainty for Gradient Aggregation in Multi-Task Learningcited by 11
  31. 2024GO4Align: Group Optimization for Multi-Task Alignmentcited by 11
  32. 2025Task Arithmetic in Trust Region: A Training-Free Model Merging Approach to Navigate Knowledge Conflictscited by 11
  33. 2025MTL-UE: Learning to Learn Nothing for Multi-Task Learningcited by 11
  34. 2024Quantifying Task Priority for Multi-Task Optimizationcited by 10
  35. 2023Improvable Gap Balancing for Multi-Task Learningcited by 9
  36. 2024Safe and Balanced: A Framework for Constrained Multi-Objective Reinforcement Learningcited by 9
  37. 2024Efficient Pareto Manifold Learning with Low-Rank Structurecited by 9
  38. 2025Commute Your Domains: Trajectory Optimality Criterion for Multi-Domain Learningcited by 9

50 most cited of 209 All 209 (JSON)