mlsanityData to 14 Oct 2026

A First Order Method for Solving Convex Bi-Level Optimization Problems

arXiv 1702.03999 ↗First posted 13 Feb 2017math.OCcited by 67

Not on the map. Why?

Abstract (arXiv)

In this paper we study convex bi-level optimization problems for which the inner level consists of minimization of the sum of smooth and nonsmooth functions. The outer level aims at minimizing a smooth and strongly convex function over the optimal solutions set of the inner problem. We analyze a first order method which is based on an existing fixed-point algorithm. Global sublinear rate of convergence of the method is established in terms of the inner objective function values.

Key facts. Cited by 67 papers in the map (data through 14 Oct 2026). First posted on arXiv 13 Feb 2017.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 10; 2022: 9; 2023: 10; 2024: 18; 2025: 8; 2026: 12.

67 papers.

Sort:

By area:

  1. 2021Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyondcited by 153
  2. 2021A Near-Optimal Algorithm for Stochastic Bilevel Optimization via Double-Momentumcited by 106
  3. 2023On Penalty-based Bilevel Gradient Descent Methodcited by 87
  4. 2021A Single-Timescale Method for Stochastic Bilevel Optimizationcited by 69
  5. 2024SEAL: Safety-enhanced Aligned LLM Fine-tuning via Bilevel Data Selectioncited by 64
  6. 2022Advancing Model Pruning via Bi-level Optimizationcited by 56
  7. 2021A Fully Single Loop Algorithm for Bilevel Optimization without Hessian Inversecited by 53
  8. 2024Principled Penalty-based Methods for Bilevel Reinforcement Learning and RLHFcited by 41
  9. 2021Randomized Stochastic Variance-Reduced Methods for Multi-Task Stochastic Bilevel Optimizationcited by 33
  10. 2023Averaged Method of Multipliers for Bi-Level Optimization without Lower-Level Strong Convexitycited by 26
  11. 2025BLUR: A Bi-Level Optimization Approach for LLM Unlearningcited by 23
  12. 2021Tighter Analysis of Alternating Stochastic Gradient Method for Stochastic Nested Problemscited by 22
38 more
  1. 2022Local Stochastic Bilevel Optimization with Momentum-Based Variance Reductioncited by 20
  2. 2022Stochastic Halpern Iteration with Variance Reduction for Stochastic Monotone Inclusionscited by 19
  3. 2022A Conditional Gradient-based Method for Simple Bilevel Optimization with Convex Lower-level Problemcited by 17
  4. 2022A Single-Timescale Analysis For Stochastic Approximation With Multiple Coupled Sequencescited by 17
  5. 2024Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomycited by 16
  6. 2024Bilevel Optimization under Unbounded Smoothness: A New Algorithm and Convergence Analysiscited by 15
  7. 2023SimFBO: Towards Simple, Flexible and Communication-efficient Federated Bilevel Learningcited by 14
  8. 2022A Primal-Dual Approach to Bilevel Optimization with Multiple Inner Minimacited by 13
  9. 2023Projection-Free Methods for Stochastic Simple Bilevel Optimization with Convex Lower-level Problemcited by 13
  10. 2025Cautious Weight Decaycited by 13
  11. 2024Stochastic Halpern iteration in normed spaces and applications to reinforcement learningcited by 12
  12. 2022Communication-Efficient Robust Federated Learning with Noisy Labelscited by 11
  13. 2023Accelerating Value Iteration with Anchoringcited by 11
  14. 2024First-Order Methods for Linearly Constrained Bilevel Optimizationcited by 10
  15. 2021Triple-level Model Inferred Collaborative Network Architecture for Video Derainingcited by 9
  16. 2024An Accelerated Algorithm for Stochastic Bilevel Optimization under Unbounded Smoothnesscited by 9
  17. 2022Algorithmic Foundations of Empirical X-risk Minimizationcited by 8
  18. 2023Communication-Efficient Federated Bilevel Optimization with Local and Global Lower Level Problemscited by 8
  19. 2025Direct Prediction Set Minimization via Bilevel Conformal Classifier Trainingcited by 8
  20. 2026Safety at One Shot: Patching Fine-Tuned LLMs with A Single Instancecited by 8
  21. 2023Convex Bi-Level Optimization Problems with Non-smooth Outer Objective Functioncited by 7
  22. 2024A Nearly Optimal Single Loop Algorithm for Stochastic Bilevel Optimization under Unbounded Smoothnesscited by 7
  23. 2021Trilevel and Multilevel Optimization using Monotone Operator Theorycited by 6
  24. 2021Optimization Induced Equilibrium Networkscited by 5
  25. 2023A Generalized Alternating Method for Bilevel Learning under the Polyak-Lojasiewicz Conditioncited by 5
  26. 2024Joint Unsupervised and Supervised Training for Automatic Speech Recognition via Bilevel Optimizationcited by 5
  27. 2024Asymptotic regularity of a generalised stochastic Halpern schemecited by 5
  28. 2021Potential Function-based Framework for Making the Gradients Small in Convex and Min-Max Optimizationcited by 4
  29. 2024Careful with that Scalpel: Improving Gradient Surgery with an EMAcited by 4
  30. 2024Revisiting Inexact Fixed-Point Iterations for Min-Max Problems: Stochasticity and Structured Nonconvexitycited by 4
  31. 2024An Accelerated Gradient Method for Convex Smooth Simple Bilevel Optimizationcited by 4
  32. 2026Direct Acceleration of Stochastic Root-Finding Without Variance Reduction and Regularizationcited by 4
  33. 2024Variance-Reduced Fast Krasnoselkii-Mann Methods for Finite-Sum Root-Finding Problemscited by 3
  34. 2025Model-Free Robust Average-Reward Reinforcement Learning with Sample Complexity Analysiscited by 3
  35. 2026Learning Policy from a Single Trajectory in Average-Reward Markov Decision Processcited by 3
  36. 2026Solving Stochastic Fixed-Point Equations with High Probabilitycited by 3
  37. 2023Achieving O(ε-1.5) Complexity in Hessian/Jacobian-free Stochastic Bilevel Optimizationcited by 2
  38. 2025Faster Fixed-Point Methods for Multichain MDPscited by 2

50 most cited of 67 All 67 (JSON)