mlsanityData to 7 Oct 2026

Multi-Objective Meta Learning

arXiv 2102.07121 ↗First posted 14 Feb 2021cs.LG cs.AIcited by 39

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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.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). Builds on 49 of its 84 references that are in the map. First posted on arXiv 14 Feb 2021.

Builds on

49 of 84 references.

References · 49

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2017Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networkscited by 4,861
  4. 2018Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentationcited by 3,210
  5. 2017Prototypical Networks for Few-shot Learningcited by 3,001
  6. 2016Perceptual Losses for Real-Time Style Transfer and Super-Resolutioncited by 2,678
  7. 2016Matching Networks for One Shot Learningcited by 2,246
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  9. 2018DARTS: Differentiable Architecture Searchcited by 1,782
  10. 2016Adversarial examples in the physical worldcited by 1,762
  11. 2017Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semanticscited by 1,345
  12. 2020Gradient Surgery for Multi-Task Learningcited by 1,210
37 more
  1. 2017Deep Hashing Network for Unsupervised Domain Adaptationcited by 1,181
  2. 2017Learning to Compare: Relation Network for Few-Shot Learningcited by 1,139
  3. 2018On First-Order Meta-Learning Algorithmscited by 1,003
  4. 2020Meta-Learning in Neural Networks: A Surveycited by 944
  5. 2018MnasNet: Platform-Aware Neural Architecture Search for Mobilecited by 937
  6. 2017A Survey on Multi-Task Learningcited by 838
  7. 2018Efficient Neural Architecture Search via Parameter Sharingcited by 831
  8. 2018Multi-Task Learning as Multi-Objective Optimizationcited by 809
  9. 2019Once-for-All: Train One Network and Specialize it for Efficient Deploymentcited by 778
  10. 2017Learning to Generalize: Meta-Learning for Domain Generalizationcited by 762
  11. 2016Deep Transfer Learning with Joint Adaptation Networkscited by 609
  12. 2014Deep Domain Confusion: Maximizing for Domain Invariancecited by 597
  13. 2018End-to-End Multi-Task Learning with Attentioncited by 533
  14. 2019Meta-Learning with Implicit Gradientscited by 523
  15. 2018FBNet: Hardware-Aware Efficient ConvNet Design via Differentiable Neural Architecture Searchcited by 480
  16. 2019Generalizing from a Few Examples: A Survey on Few-Shot Learningcited by 462
  17. 2018Bilevel Programming for Hyperparameter Optimization and Meta-Learningcited by 403
  18. 2019Semi-supervised Domain Adaptation via Minimax Entropycited by 333
  19. 2018SNAS: Stochastic Neural Architecture Searchcited by 288
  20. 2016Hyperparameter optimization with approximate gradientcited by 231
  21. 2016Learning to Optimizecited by 195
  22. 2018Truncated Back-propagation for Bilevel Optimizationcited by 187
  23. 2018Meta-Gradient Reinforcement Learningcited by 156
  24. 2019On the Convergence Theory of Gradient-Based Model-Agnostic Meta-Learning Algorithmscited by 132
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  27. 2020A Generic First-Order Algorithmic Framework for Bi-Level Programming Beyond Lower-Level Singletoncited by 78
  28. 2020NSGANetV2: Evolutionary Multi-Objective Surrogate-Assisted Neural Architecture Searchcited by 75
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  30. 2020Attract, Perturb, and Explore: Learning a Feature Alignment Network for Semi-supervised Domain Adaptationcited by 69
  31. 2020Online Meta-Learning for Multi-Source and Semi-Supervised Domain Adaptationcited by 64
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  33. 2018Few-Shot Learning with Metric-Agnostic Conditional Embeddingscited by 40
  34. 2018Meta-Learning for Multi-objective Reinforcement Learningcited by 33
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 4; 2023: 11; 2024: 8; 2025: 9; 2026: 6.

39 papers.

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  1. 2021Reasonable Effectiveness of Random Weighting: A Litmus Test for Multi-Task Learningcited by 100
  2. 2022Auto-Lambda: Disentangling Dynamic Task Relationshipscited by 73
  3. 2023Three-Way Trade-Off in Multi-Objective Learning: Optimization, Generalization and Conflict-Avoidancecited by 35
  4. 2023Direction-oriented Multi-objective Learning: Simple and Provable Stochastic Algorithmscited by 33
  5. 2023Dual-Balancing for Multi-Task Learningcited by 27
  6. 2025PARM: Multi-Objective Test-Time Alignment via Preference-Aware Autoregressive Reward Modelcited by 27
  7. 2024Robust Multi-Task Learning with Excess Riskscited by 23
  8. 2024MTMamba: Enhancing Multi-Task Dense Scene Understanding by Mamba-Based Decoderscited by 22
  9. 2023FedHCA2: Towards Hetero-Client Federated Multi-Task Learningcited by 17
  10. 2025Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyondcited by 15
  11. 2022Stochastic Multiple Target Sampling Gradient Descentcited by 14
  12. 2022Mitigating Gradient Bias in Multi-objective Learning: A Provably Convergent Stochastic Approachcited by 14
27 more
  1. 2023Effective Structured Prompting by Meta-Learning and Representative Verbalizercited by 14
  2. 2024MTMamba++: Enhancing Multi-Task Dense Scene Understanding via Mamba-Based Decoderscited by 10
  3. 2023Improvable Gap Balancing for Multi-Task Learningcited by 9
  4. 2024A First-Order Multi-Gradient Algorithm for Multi-Objective Bi-Level Optimizationcited by 8
  5. 2024Swiss Army Knife: Synergizing Biases in Knowledge from Vision Foundation Models for Multi-Task Learningcited by 6
  6. 2023BYOM: Building Your Own Multi-Task Model For Freecited by 5
  7. 2022Generalization In Multi-Objective Machine Learningcited by 4
  8. 2025MOORL: A Framework for Integrating Offline-Online Reinforcement Learningcited by 4
  9. 2023Bi-level Multi-objective Evolutionary Learning: A Case Study on Multi-task Graph Neural Topology Searchcited by 3
  10. 2023Decomposition Ascribed Synergistic Learning for Unified Image Restorationcited by 3
  11. 2024Multi-Task Learning with Multi-Task Optimizationcited by 3
  12. 2026UniARM: Towards a Unified Autoregressive Reward Model for Multi-Objective Test-Time Alignmentcited by 3
  13. 2023Generating Adversarial Examples with Task Oriented Multi-Objective Optimizationcited by 2
  14. 2023Examining Common Paradigms in Multi-Task Learningcited by 2
  15. 2025Deciphering Trajectory-Aided LLM Reasoning: An Optimization Perspectivecited by 2
  16. 2025AutoScale: Linear Scalarization Guided by Multi-Task Optimization Metricscited by 2
  17. 2025Multi-Objective Bilevel Learningcited by 2
  18. 2024Robust Analysis of Multi-Task Learning Efficiency: New Benchmarks on Light-Weighed Backbones and Effective Measurement of Multi-Task Learning Challenges by Feature Disentanglementcited by 1
  19. 2024Enhancing Sharpness-Aware Minimization by Learning Perturbation Radiuscited by 1
  20. 2025Multi-Objective Reinforcement Learning for Large Language Model Optimization: Visionary Perspectivecited by 1
  21. 2026A Tale of Two Problems: Multi-Task Bilevel Learning Meets Equality Constrained Multi-Objective Optimizationcited by 1
  22. 2025VirnyFlow: Optimizing ML Pipelines for Accuracy, Fairness, and Stability at Scalecited by 0
  23. 2025AutoBalance: An Automatic Balancing Framework for Training Physics-Informed Neural Networkscited by 0
  24. 2026CORE-MTL: Rethinking Gradient Balancing via Causal Orthogonal Representationscited by 0
  25. 2026Multi-Objective Exploration and Preference Optimization via Mutual Informationcited by 0
  26. 2026Regularity-Aware Stochastic MGDA with Adaptive Conflict-Avoidant Update Direction Controlcited by 0
  27. 2026Efficient Hessian-Free Methods for Multi-Objective Bilevel Optimization with Nonconvex Lower Levelcited by 0