# Multi-Objective Meta Learning

arXiv: https://arxiv.org/abs/2102.07121 · HTML: https://mlsanity.com/paper/2102.07121/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 84 references that are in the map.
- First posted on arXiv 14 Feb 2021.

## Builds on (most cited first, 30 of 49)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [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)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [MnasNet: Platform-Aware Neural Architecture Search for Mobile](https://mlsanity.com/paper/1807.11626/) (2018)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [Efficient Neural Architecture Search via Parameter Sharing](https://mlsanity.com/paper/1802.03268/) (2018)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Once-for-All: Train One Network and Specialize it for Efficient Deployment](https://mlsanity.com/paper/1908.09791/) (2019)
- [Learning to Generalize: Meta-Learning for Domain Generalization](https://mlsanity.com/paper/1710.03463/) (2017)
- [Deep Transfer Learning with Joint Adaptation Networks](https://mlsanity.com/paper/1605.06636/) (2016)
- [Deep Domain Confusion: Maximizing for Domain Invariance](https://mlsanity.com/paper/1412.3474/) (2014)
- [End-to-End Multi-Task Learning with Attention](https://mlsanity.com/paper/1803.10704/) (2018)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [FBNet: Hardware-Aware Efficient ConvNet Design via Differentiable Neural Architecture Search](https://mlsanity.com/paper/1812.03443/) (2018)
- [Generalizing from a Few Examples: A Survey on Few-Shot Learning](https://mlsanity.com/paper/1904.05046/) (2019)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Semi-supervised Domain Adaptation via Minimax Entropy](https://mlsanity.com/paper/1904.06487/) (2019)

## Built on by (most cited first, 30 of 39)

- [Reasonable Effectiveness of Random Weighting: A Litmus Test for Multi-Task Learning](https://mlsanity.com/paper/2111.10603/) (2021)
- [Auto-Lambda: Disentangling Dynamic Task Relationships](https://mlsanity.com/paper/2202.03091/) (2022)
- [Three-Way Trade-Off in Multi-Objective Learning: Optimization, Generalization and Conflict-Avoidance](https://mlsanity.com/paper/2305.20057/) (2023)
- [Direction-oriented Multi-objective Learning: Simple and Provable Stochastic Algorithms](https://mlsanity.com/paper/2305.18409/) (2023)
- [PARM: Multi-Objective Test-Time Alignment via Preference-Aware Autoregressive Reward Model](https://mlsanity.com/paper/2505.06274/) (2025)
- [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)
- [MTMamba: Enhancing Multi-Task Dense Scene Understanding by Mamba-Based Decoders](https://mlsanity.com/paper/2407.02228/) (2024)
- [Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyond](https://mlsanity.com/paper/2501.10945/) (2025)
- [FedHCA2: Towards Hetero-Client Federated Multi-Task Learning](https://mlsanity.com/paper/2311.13250/) (2023)
- [Stochastic Multiple Target Sampling Gradient Descent](https://mlsanity.com/paper/2206.01934/) (2022)
- [Mitigating Gradient Bias in Multi-objective Learning: A Provably Convergent Stochastic Approach](https://mlsanity.com/paper/2210.12624/) (2022)
- [Effective Structured Prompting by Meta-Learning and Representative Verbalizer](https://mlsanity.com/paper/2306.00618/) (2023)
- [MTMamba++: Enhancing Multi-Task Dense Scene Understanding via Mamba-Based Decoders](https://mlsanity.com/paper/2408.15101/) (2024)
- [Improvable Gap Balancing for Multi-Task Learning](https://mlsanity.com/paper/2307.15429/) (2023)
- [A First-Order Multi-Gradient Algorithm for Multi-Objective Bi-Level Optimization](https://mlsanity.com/paper/2401.09257/) (2024)
- [Swiss Army Knife: Synergizing Biases in Knowledge from Vision Foundation Models for Multi-Task Learning](https://mlsanity.com/paper/2410.14633/) (2024)
- [BYOM: Building Your Own Multi-Task Model For Free](https://mlsanity.com/paper/2310.01886/) (2023)
- [Generalization In Multi-Objective Machine Learning](https://mlsanity.com/paper/2208.13499/) (2022)
- [MOORL: A Framework for Integrating Offline-Online Reinforcement Learning](https://mlsanity.com/paper/2506.09574/) (2025)
- [Bi-level Multi-objective Evolutionary Learning: A Case Study on Multi-task Graph Neural Topology Search](https://mlsanity.com/paper/2302.02565/) (2023)
- [Decomposition Ascribed Synergistic Learning for Unified Image Restoration](https://mlsanity.com/paper/2308.00759/) (2023)
- [Multi-Task Learning with Multi-Task Optimization](https://mlsanity.com/paper/2403.16162/) (2024)
- [UniARM: Towards a Unified Autoregressive Reward Model for Multi-Objective Test-Time Alignment](https://mlsanity.com/paper/2602.09538/) (2026)
- [Generating Adversarial Examples with Task Oriented Multi-Objective Optimization](https://mlsanity.com/paper/2304.13229/) (2023)
- [Examining Common Paradigms in Multi-Task Learning](https://mlsanity.com/paper/2311.04698/) (2023)
- [Deciphering Trajectory-Aided LLM Reasoning: An Optimization Perspective](https://mlsanity.com/paper/2505.19815/) (2025)
- [AutoScale: Linear Scalarization Guided by Multi-Task Optimization Metrics](https://mlsanity.com/paper/2508.13979/) (2025)
- [Multi-Objective Bilevel Learning](https://mlsanity.com/paper/2511.07824/) (2025)
- [Robust Analysis of Multi-Task Learning Efficiency: New Benchmarks on Light-Weighed Backbones and Effective Measurement of Multi-Task Learning Challenges by Feature Disentanglement](https://mlsanity.com/paper/2402.03557/) (2024)

## Abstract (arXiv)

Meta learning with multiple objectives can be formulated as a Multi-Objective Bi-Level optimization Problem (MOBLP) where the upper-level subproblem is to solve several possible conflicting targets for the meta learner. However, existing studies either apply an inefficient evolutionary algorithm or linearly combine multiple objectives as a single-objective problem with the need to tune combination weights. In this paper, we propose a unified gradient-based Multi-Objective Meta Learning (MOML) framework and devise the first gradient-based optimization algorithm to solve the MOBLP by alternatively solving the lower-level and upper-level subproblems via the gradient descent method and the gradient-based multi-objective optimization method, respectively. Theoretically, we prove the convergence properties of the proposed gradient-based optimization algorithm. Empirically, we show the effectiveness of the proposed MOML framework in several meta learning problems, including few-shot learning, neural architecture search, domain adaptation, and multi-task learning.