# Conflict-Averse Gradient Descent for Multi-task Learning

arXiv: https://arxiv.org/abs/2110.14048 · HTML: https://mlsanity.com/paper/2110.14048/

## Key facts

- Cited by 459 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 48 references that are in the map.
- First posted on arXiv 26 Oct 2021.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [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)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [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)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Taskonomy: Disentangling Task Transfer Learning](https://mlsanity.com/paper/1804.08328/) (2018)
- [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)
- [Policy Distillation](https://mlsanity.com/paper/1511.06295/) (2015)
- [Distral: Robust Multitask Reinforcement Learning](https://mlsanity.com/paper/1707.04175/) (2017)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [Just Pick a Sign: Optimizing Deep Multitask Models with Gradient Sign Dropout](https://mlsanity.com/paper/2010.06808/) (2020)
- [Actor-Mimic: Deep Multitask and Transfer Reinforcement Learning](https://mlsanity.com/paper/1511.06342/) (2015)
- [Multi-Task Reinforcement Learning with Context-based Representations](https://mlsanity.com/paper/2102.06177/) (2021)
- [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)
- [Routing Networks: Adaptive Selection of Non-linear Functions for Multi-Task Learning](https://mlsanity.com/paper/1711.01239/) (2017)
- [A Joint Many-Task Model: Growing a Neural Network for Multiple NLP Tasks](https://mlsanity.com/paper/1611.01587/) (2016)
- [Certified Monotonic Neural Networks](https://mlsanity.com/paper/2011.10219/) (2020)
- [Divide-and-Conquer Reinforcement Learning](https://mlsanity.com/paper/1711.09874/) (2017)
- [Auxiliary Task Reweighting for Minimum-data Learning](https://mlsanity.com/paper/2010.08244/) (2020)

## Built on by (most cited first, 30 of 459)

- [AdaMerging: Adaptive Model Merging for Multi-Task Learning](https://mlsanity.com/paper/2310.02575/) (2023)
- [Rewarded soups: towards Pareto-optimal alignment by interpolating weights fine-tuned on diverse rewards](https://mlsanity.com/paper/2306.04488/) (2023)
- [Twin-Merging: Dynamic Integration of Modular Expertise in Model Merging](https://mlsanity.com/paper/2406.15479/) (2024)
- [Diffusion Model is an Effective Planner and Data Synthesizer for Multi-Task Reinforcement Learning](https://mlsanity.com/paper/2305.18459/) (2023)
- [Reasonable Effectiveness of Random Weighting: A Litmus Test for Multi-Task Learning](https://mlsanity.com/paper/2111.10603/) (2021)
- [Representation Surgery for Multi-Task Model Merging](https://mlsanity.com/paper/2402.02705/) (2024)
- [Diffusion Models for Reinforcement Learning: A Survey](https://mlsanity.com/paper/2311.01223/) (2023)
- [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)
- [In Defense of the Unitary Scalarization for Deep Multi-Task Learning](https://mlsanity.com/paper/2201.04122/) (2022)
- [A Survey on All-in-One Image Restoration: Taxonomy, Evaluation and Future Trends](https://mlsanity.com/paper/2410.15067/) (2024)
- [Erasing Undesirable Influence in Diffusion Models](https://mlsanity.com/paper/2401.05779/) (2024)
- [Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective](https://mlsanity.com/paper/2502.00604/) (2025)
- [Smooth Tchebycheff Scalarization for Multi-Objective Optimization](https://mlsanity.com/paper/2402.19078/) (2024)
- [MetaGPT: Merging Large Language Models Using Model Exclusive Task Arithmetic](https://mlsanity.com/paper/2406.11385/) (2024)
- [Recon: Reducing Conflicting Gradients from the Root for Multi-Task Learning](https://mlsanity.com/paper/2302.11289/) (2023)
- [Revisiting Scalarization in Multi-Task Learning: A Theoretical Perspective](https://mlsanity.com/paper/2308.13985/) (2023)
- [Localize-and-Stitch: Efficient Model Merging via Sparse Task Arithmetic](https://mlsanity.com/paper/2408.13656/) (2024)
- [ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks](https://mlsanity.com/paper/2408.11104/) (2024)
- [TaskExpert: Dynamically Assembling Multi-Task Representations with Memorial Mixture-of-Experts](https://mlsanity.com/paper/2307.15324/) (2023)
- [MTLoRA: A Low-Rank Adaptation Approach for Efficient Multi-Task Learning](https://mlsanity.com/paper/2403.20320/) (2024)
- [One Model is All You Need: Multi-Task Learning Enables Simultaneous Histology Image Segmentation and Classification](https://mlsanity.com/paper/2203.00077/) (2022)
- [HumanBench: Towards General Human-centric Perception with Projector Assisted Pretraining](https://mlsanity.com/paper/2303.05675/) (2023)
- [MotionGPT3: Human Motion as a Second Modality](https://mlsanity.com/paper/2506.24086/) (2025)
- [Three-Way Trade-Off in Multi-Objective Learning: Optimization, Generalization and Conflict-Avoidance](https://mlsanity.com/paper/2305.20057/) (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)

## Abstract (arXiv)

The goal of multi-task learning is to enable more efficient learning than single task learning by sharing model structures for a diverse set of tasks. A standard multi-task learning objective is to minimize the average loss across all tasks. While straightforward, using this objective often results in much worse final performance for each task than learning them independently. A major challenge in optimizing a multi-task model is the conflicting gradients, where gradients of different task objectives are not well aligned so that following the average gradient direction can be detrimental to specific tasks' performance. Previous work has proposed several heuristics to manipulate the task gradients for mitigating this problem. But most of them lack convergence guarantee and/or could converge to any Pareto-stationary point. In this paper, we introduce Conflict-Averse Gradient descent (CAGrad) which minimizes the average loss function, while leveraging the worst local improvement of individual tasks to regularize the algorithm trajectory. CAGrad balances the objectives automatically and still provably converges to a minimum over the average loss. It includes the regular gradient descent (GD) and the multiple gradient descent algorithm (MGDA) in the multi-objective optimization (MOO) literature as special cases. On a series of challenging multi-task supervised learning and reinforcement learning tasks, CAGrad achieves improved performance over prior state-of-the-art multi-objective gradient manipulation methods.