mlsanityData to 7 Oct 2026

Functional Bilevel Optimization for Machine Learning

arXiv 2403.20233 ↗First posted 29 Mar 2024stat.ML cs.LGcited by 20

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Abstract (arXiv)

In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods developed in the parametric setting, where the inner objective is strongly convex with respect to the parameters of the prediction function. The functional point of view does not rely on this assumption and notably allows using over-parameterized neural networks as the inner prediction function. We propose scalable and efficient algorithms for the functional bilevel optimization problem and illustrate the benefits of our approach on instrumental regression and reinforcement learning tasks.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Builds on 57 of its 98 references that are in the map. First posted on arXiv 29 Mar 2024.

Builds on

57 of 98 references.

References · 57

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2019Invariant Risk Minimizationcited by 1,832
  4. 2018Demystifying MMD GANscited by 1,268
  5. 2016HyperNetworkscited by 1,003
  6. 2015Automatic differentiation in machine learning: a surveycited by 846
  7. 2018A Convergence Theory for Deep Learning via Over-Parameterizationcited by 784
  8. 2018Gradient Descent Finds Global Minima of Deep Neural Networkscited by 572
  9. 2018Meta-learning with differentiable closed-form solverscited by 395
  10. 2019Optimizing Millions of Hyperparameters by Implicit Differentiationcited by 303
  11. 2020Scalable Gradients for Stochastic Differential Equationscited by 264
  12. 2017Forward and Reverse Gradient-Based Hyperparameter Optimizationcited by 232
38 more
  1. 2016Hyperparameter optimization with approximate gradientcited by 231
  2. 2018Approximation Methods for Bilevel Programmingcited by 231
  3. 2020Loss landscapes and optimization in over-parameterized non-linear systems and neural networkscited by 231
  4. 2020Bilevel Optimization: Convergence Analysis and Enhanced Designcited by 219
  5. 2017SMASH: One-Shot Model Architecture Search through HyperNetworkscited by 200
  6. 2021Efficient and Modular Implicit Differentiationcited by 199
  7. 2020Invariant Risk Minimization Gamescited by 188
  8. 2018Truncated Back-propagation for Bilevel Optimizationcited by 187
  9. 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 183
  10. 2020On the Iteration Complexity of Hypergradient Computationcited by 154
  11. 2021Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyondcited by 151
  12. 2019Neural Jump Stochastic Differential Equationscited by 147
  13. 2020A Two-Timescale Framework for Bilevel Optimization: Complexity Analysis and Application to Actor-Criticcited by 141
  14. 2018Graph HyperNetworks for Neural Architecture Searchcited by 131
  15. 2019Kernel Instrumental Variable Regressioncited by 118
  16. 2016On Differentiating Parameterized Argmin and Argmax Problems with Application to Bi-level Optimizationcited by 108
  17. 2019Self-Tuning Networks: Bilevel Optimization of Hyperparameters using Structured Best-Response Functionscited by 104
  18. 2023On Penalty-based Bilevel Gradient Descent Methodcited by 87
  19. 2022Tutorial on amortized optimizationcited by 83
  20. 2018Reviving and Improving Recurrent Back-Propagationcited by 69
  21. 2020Learning Deep Features in Instrumental Variable Regressioncited by 65
  22. 2021Towards Gradient-based Bilevel Optimization with Non-convex Followers and Beyondcited by 62
  23. 2021Amortized Implicit Differentiation for Stochastic Bilevel Optimizationcited by 62
  24. 2023On Penalty Methods for Nonconvex Bilevel Optimization and First-Order Stochastic Approximationcited by 50
  25. 2020Auxiliary Learning by Implicit Differentiationcited by 45
  26. 2021Nonsmooth Implicit Differentiation for Machine Learning and Optimizationcited by 43
  27. 2021Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluationcited by 39
  28. 2023A Guide Through the Zoo of Biased SGDcited by 39
  29. 2021Control-Oriented Model-Based Reinforcement Learning with Implicit Differentiationcited by 35
  30. 2023One-step differentiation of iterative algorithmscited by 28
  31. 2023Averaged Method of Multipliers for Bi-Level Optimization without Lower-Level Strong Convexitycited by 26
  32. 2022Automatic differentiation of nonsmooth iterative algorithmscited by 25
  33. 2022Non-Convex Bilevel Games with Critical Point Selection Mapscited by 25
  34. 2020Super-efficiency of automatic differentiation for functions defined as a minimumcited by 24
  35. 2021Value-Function-based Sequential Minimization for Bi-level Optimizationcited by 24
  36. 2024Implicit Diffusion: Efficient Optimization through Stochastic Samplingcited by 22
  37. 2022Offline Reinforcement Learning with Instrumental Variables in Confounded Markov Decision Processescited by 19
  38. 2020Delta-STN: Efficient Bilevel Optimization for Neural Networks using Structured Response Jacobianscited by 17

50 most cited of 57 All 57 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 11; 2026: 7.

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  1. 2025Cautious Weight Decaycited by 12
  2. 2024Nonparametric Instrumental Regression via Kernel Methods is Minimax Optimalcited by 7
  3. 2024CoBo: Collaborative Learning via Bilevel Optimizationcited by 5
  4. 2025A First-order Generative Bilevel Optimization Framework for Diffusion Modelscited by 4
  5. 2025Demystifying Spectral Feature Learning for Instrumental Variable Regressioncited by 4
  6. 2025Optimality and Adaptivity of Deep Neural Features for Instrumental Variable Regressioncited by 3
  7. 2025Closed-Form Last Layer Optimizationcited by 3
  8. 2025A Fully First-Order Layer for Differentiable Optimizationcited by 3
  9. 2025Learning Theory for Kernel Bilevel Optimizationcited by 2
  10. 2025Outcome-Aware Spectral Feature Learning for Instrumental Variable Regressioncited by 2
  11. 2026Non-Stationary Functional Bilevel Optimizationcited by 2
  12. 2025Stackelberg Coupling of Online Representation Learning and Reinforcement Learningcited by 1
8 more
  1. 2026Efficiency Follows Global-Local Decouplingcited by 1
  2. 2026Functional Natural Policy Gradientscited by 1
  3. 2026Functional Gradient Descent with Adaptive Representationscited by 1
  4. 2026AIFS-SUBS: Extending Data-Driven Forecasting to Sub-Seasonal Timescalescited by 1
  5. 2025From Data to Rewards: a Bilevel Optimization Perspective on Maximum Likelihood Estimationcited by 0
  6. 2025Bridging Constraints and Stochasticity: A Fully First-Order Method for Stochastic Bilevel Optimization with Linear Constraintscited by 0
  7. 2026ROAD: Adaptive Data Mixing for Offline-to-Online Reinforcement Learning via Bi-Level Optimizationcited by 0
  8. 2026Semiparametric Efficient Bilevel Gradient Estimationcited by 0