mlsanityData to 7 Oct 2026

Efficient Gradient Approximation Method for Constrained Bilevel Optimization

arXiv 2302.01970 ↗First posted 3 Feb 2023cs.LGcited by 15

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Abstract (arXiv)

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with equality and inequality constraints and the upper-level optimization problem is non-convex. The overall objective function is non-convex and non-differentiable. To solve the problem, we develop a gradient-based approach, called gradient approximation method, which determines the descent direction by computing several representative gradients of the objective function inside a neighborhood of the current estimate. We show that the algorithm asymptotically converges to the set of Clarke stationary points, and demonstrate the efficacy of the algorithm by the experiments on hyperparameter optimization and meta-learning.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). Builds on 28 of its 72 references that are in the map. First posted on arXiv 3 Feb 2023.

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28 of 72 references.

References · 28

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16 more
  1. 2018Bilevel Programming for Hyperparameter Optimization and Meta-Learningcited by 403
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 8; 2025: 3; 2026: 3.

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  1. 2024Constrained Bi-Level Optimization: Proximal Lagrangian Value function Approach and Hessian-free Algorithmcited by 16
  2. 2024First-Order Methods for Linearly Constrained Bilevel Optimizationcited by 10
  3. 2024A Primal-Dual-Assisted Penalty Approach to Bilevel Optimization with Coupled Constraintscited by 7
  4. 2024In-Trajectory Inverse Reinforcement Learning: Learn Incrementally Before An Ongoing Trajectory Terminatescited by 7
  5. 2023You Shall Pass: Dealing with the Zero-Gradient Problem in Predict and Optimize for Convex Optimizationcited by 3
  6. 2024Differentially Private Bilevel Optimizationcited by 2
  7. 2024Meta-Reinforcement Learning with Universal Policy Adaptation: Provable Near-Optimality under All-task Optimum Comparatorcited by 2
  8. 2025Safe Gradient Flow for Bilevel Optimizationcited by 1
  9. 2025Explainable reinforcement learning from human feedback to improve alignmentcited by 1
  10. 2026Penalty-Based First-Order Methods for Bilevel Optimization with Minimax and Constrained Lower-Level Problemscited by 1
  11. 2024Riemannian Bilevel Optimizationcited by 0
  12. 2024Double Momentum Method for Lower-Level Constrained Bilevel Optimizationcited by 0
3 more
  1. 2025A Single-Loop First-Order Algorithm for Linearly Constrained Bilevel Optimizationcited by 0
  2. 2026Sample Complexity Analysis for Constrained Bilevel Reinforcement Learningcited by 0
  3. 2026Interactive Inverse Reinforcement Learning of Interaction Scenarios via Bi-level Optimizationcited by 0