mlsanityData to 7 Oct 2026

Learning to Solve Constrained Bilevel Control Co-Design Problems

arXiv 2507.09050 ↗First posted 11 Jul 2025math.OC cs.LGcited by 0

Not on the map. Why?

Abstract (arXiv)

Learning to Optimize (L2O) is a subfield of machine learning (ML) in which ML models are trained to solve parametric optimization problems. The general goal is to learn a fast approximator of solutions to constrained optimization problems, as a function of their defining parameters. Prior L2O methods focus almost entirely on single-level programs, in contrast to the bilevel programs, whose constraints are themselves expressed in terms of optimization subproblems. Bilevel programs have numerous important use cases but are notoriously difficult to solve, particularly under stringent time demands. This paper proposes a framework for learning to solve a broad class of challenging bilevel optimization problems, by leveraging modern techniques for differentiation through optimization problems. The framework is illustrated on an array of synthetic bilevel programs, as well as challenging control system co-design problems, showing how neural networks can be trained as efficient approximators of parametric bilevel optimization.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 27 of its 52 references that are in the map. First posted on arXiv 11 Jul 2025.

Builds on

27 of 52 references.

References · 27

  1. 2016Learning to learn by gradient descent by gradient descentcited by 616
  2. 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 612
  3. 2019Differentiable Convex Optimization Layerscited by 458
  4. 2018Approximation Methods for Bilevel Programmingcited by 231
  5. 2018Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimizationcited by 220
  6. 2021DC3: A learning method for optimization with hard constraintscited by 181
  7. 2021End-to-End Constrained Optimization Learning: A Surveycited by 154
  8. 2017A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applicationscited by 126
  9. 2019Reinforcement Learning for Integer Programming: Learning to Cutcited by 108
  10. 2019Deep Declarative Networks: A New Hopecited by 77
  11. 2019Differentiating Through a Cone Programcited by 72
  12. 2020Lagrangian Duality for Constrained Deep Learningcited by 72
15 more
  1. 2022Self-Supervised Primal-Dual Learning for Constrained Optimizationcited by 60
  2. 2019Online Mixed-Integer Optimization in Millisecondscited by 37
  3. 2023End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatchcited by 35
  4. 2023Learning to Warm-Start Fixed-Point Optimization Algorithmscited by 32
  5. 2023RAYEN: Imposition of Hard Convex Constraints on Neural Networkscited by 30
  6. 2022End-to-End Learning to Warm-Start for Real-Time Quadratic Optimizationcited by 25
  7. 2018Solution Refinement at Regular Points of Conic Problemscited by 21
  8. 2020Learning Convex Optimization Modelscited by 16
  9. 2018Statistical Learning For DC Optimal Power Flowcited by 12
  10. 2023A New Computationally Simple Approach for Implementing Neural Networks with Output Hard Constraintscited by 12
  11. 2023Co-Design Optimisation of Morphing Topology and Control of Winged Dronescited by 4
  12. 2025Efficient Primal Heuristics for Mixed Binary Quadratic Programs Using Suboptimal Rounding Guidancecited by 3
  13. 2013Efficient Evolutionary Algorithm for Single-Objective Bilevel Optimizationcited by 2
  14. 2021Constraint-Handling Techniques for Particle Swarm Optimization Algorithmscited by 2
  15. 2025Perturbed Gradient Descent via Convex Quadratic Approximation for Nonconvex Bilevel Optimizationcited by 2

Built on by

Not cited yet.