mlsanityData to 14 Oct 2026

A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications

arXiv 1705.06270 ↗First posted 17 May 2017math.OC cs.NEcited by 129

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Abstract (arXiv)

Bilevel optimization is defined as a mathematical program, where an optimization problem contains another optimization problem as a constraint. These problems have received significant attention from the mathematical programming community. Only limited work exists on bilevel problems using evolutionary computation techniques; however, recently there has been an increasing interest due to the proliferation of practical applications and the potential of evolutionary algorithms in tackling these problems. This paper provides a comprehensive review on bilevel optimization from the basic principles to solution strategies; both classical and evolutionary. A number of potential application problems are also discussed. To offer the readers insights on the prominent developments in the field of bilevel optimization, we have performed an automated text-analysis of an extended list of papers published on bilevel optimization to date. This paper should motivate evolutionary computation researchers to pay more attention to this practical yet challenging area.

Key facts. Cited by 129 papers in the map (data through 14 Oct 2026). First posted on arXiv 17 May 2017.

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Citing papers per year: 2019: 1; 2020: 0; 2021: 14; 2022: 24; 2023: 30; 2024: 31; 2025: 17; 2026: 12.

129 papers.

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  1. 2021Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyondcited by 153
  2. 2024EraseAnything: Enabling Concept Erasure in Rectified Flow Transformerscited by 95
  3. 2024LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discoverycited by 86
  4. 2022FedNest: Federated Bilevel, Minimax, and Compositional Optimizationcited by 60
  5. 2023On Penalty Methods for Nonconvex Bilevel Optimization and First-Order Stochastic Approximationcited by 51
  6. 2022Self-Guided Noise-Free Data Generation for Efficient Zero-Shot Learningcited by 50
  7. 2023Class-Incremental Exemplar Compression for Class-Incremental Learningcited by 50
  8. 2022AutoBalance: Optimized Loss Functions for Imbalanced Datacited by 49
  9. 2023Model Agnostic Sample Reweighting for Out-of-Distribution Learningcited by 44
  10. 2023First-order penalty methods for bilevel optimizationcited by 41
  11. 2023An Introduction to Bi-level Optimization: Foundations and Applications in Signal Processing and Machine Learningcited by 41
  12. 2022On Implicit Bias in Overparameterized Bilevel Optimizationcited by 30
38 more
  1. 2023Learning to Retain while Acquiring: Combating Distribution-Shift in Adversarial Data-Free Knowledge Distillationcited by 29
  2. 2024Unleashing the Power of Data Tsunami: A Comprehensive Survey on Data Assessment and Selection for Instruction Tuning of Language Modelscited by 29
  3. 2023Probabilistic Bilevel Coreset Selectioncited by 27
  4. 2021Safe Pontryagin Differentiable Programmingcited by 26
  5. 2022Gradient-based Bi-level Optimization for Deep Learning: A Surveycited by 26
  6. 2024Bridging Evolutionary Algorithms and Reinforcement Learning: A Comprehensive Survey on Hybrid Algorithmscited by 26
  7. 2023Learngene: Inheriting Condensed Knowledge from the Ancestry Model to Descendant Modelscited by 24
  8. 2023FairTune: Optimizing Parameter Efficient Fine Tuning for Fairness in Medical Image Analysiscited by 23
  9. 2024A Survey of Optimization-based Task and Motion Planning: From Classical To Learning Approachescited by 20
  10. 2019Learner-aware Teaching: Inverse Reinforcement Learning with Preferences and Constraintscited by 18
  11. 2025Systemizing Multiplicity: The Curious Case of Arbitrariness in Machine Learningcited by 17
  12. 2022Learning to Split for Automatic Bias Detectioncited by 16
  13. 2024Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomycited by 16
  14. 2022Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methodscited by 15
  15. 2022Single Time-scale Actor-critic Method to Solve the Linear Quadratic Regulator with Convergence Guaranteescited by 14
  16. 2023SimFBO: Towards Simple, Flexible and Communication-efficient Federated Bilevel Learningcited by 14
  17. 2022Asynchronous Distributed Bilevel Optimizationcited by 13
  18. 2023Communication-Efficient Federated Hypergradient Computation via Aggregated Iterative Differentiationcited by 13
  19. 2023Non-Exemplar Online Class-incremental Continual Learning via Dual-prototype Self-augment and Refinementcited by 13
  20. 2023Symmetry-Aware Robot Design with Structured Subgroupscited by 13
  21. 2023Refined Coreset Selection: Towards Minimal Coreset Size under Model Performance Constraintscited by 13
  22. 2025Quantized Spike-driven Transformercited by 13
  23. 2021Knowledge-Enhanced Top-K Recommendation in Poincar'e Ballcited by 12
  24. 2021A Gradient Method for Multilevel Optimizationcited by 12
  25. 2021Half a Dozen Real-World Applications of Evolutionary Multitasking, and Morecited by 12
  26. 2023Auxiliary Learning as an Asymmetric Bargaining Gamecited by 12
  27. 2021Probabilistic Metric Learning with Adaptive Margin for Top-K Recommendationcited by 11
  28. 2021Inexact bilevel stochastic gradient methods for constrained and unconstrained lower-level problemscited by 11
  29. 2024Efficient Prior Calibration From Indirect Datacited by 11
  30. 2024Memory-Efficient Gradient Unrolling for Large-Scale Bi-level Optimizationcited by 11
  31. 2026Why AI systems don't learn and what to do about it: Lessons on autonomous learning from cognitive sciencecited by 11
  32. 2021Fair Clustering Using Antidote Datacited by 10
  33. 2022Image quality assessment for machine learning tasks using meta-reinforcement learningcited by 10
  34. 2022Alternating Implicit Projected SGD and Its Efficient Variants for Equality-constrained Bilevel Optimizationcited by 10
  35. 2023Sharpness-Aware Data Poisoning Attackcited by 10
  36. 2024First-Order Methods for Linearly Constrained Bilevel Optimizationcited by 10
  37. 2025Optimizing Decomposition for Optimal Claim Verificationcited by 10
  38. 2021Characterizing the Gap Between Actor-Critic and Policy Gradientcited by 9

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