# Learning to Solve Constrained Bilevel Control Co-Design Problems

arXiv: https://arxiv.org/abs/2507.09050 · HTML: https://mlsanity.com/paper/2507.09050/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 52 references that are in the map.
- First posted on arXiv 11 Jul 2025.

## Builds on (most cited first, 27 of 27)

- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Approximation Methods for Bilevel Programming](https://mlsanity.com/paper/1802.02246/) (2018)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications](https://mlsanity.com/paper/1705.06270/) (2017)
- [Reinforcement Learning for Integer Programming: Learning to Cut](https://mlsanity.com/paper/1906.04859/) (2019)
- [Deep Declarative Networks: A New Hope](https://mlsanity.com/paper/1909.04866/) (2019)
- [Lagrangian Duality for Constrained Deep Learning](https://mlsanity.com/paper/2001.09394/) (2020)
- [Differentiating Through a Cone Program](https://mlsanity.com/paper/1904.09043/) (2019)
- [Self-Supervised Primal-Dual Learning for Constrained Optimization](https://mlsanity.com/paper/2208.09046/) (2022)
- [Online Mixed-Integer Optimization in Milliseconds](https://mlsanity.com/paper/1907.02206/) (2019)
- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [Learning to Warm-Start Fixed-Point Optimization Algorithms](https://mlsanity.com/paper/2309.07835/) (2023)
- [RAYEN: Imposition of Hard Convex Constraints on Neural Networks](https://mlsanity.com/paper/2307.08336/) (2023)
- [End-to-End Learning to Warm-Start for Real-Time Quadratic Optimization](https://mlsanity.com/paper/2212.08260/) (2022)
- [Solution Refinement at Regular Points of Conic Problems](https://mlsanity.com/paper/1811.02157/) (2018)
- [Learning Convex Optimization Models](https://mlsanity.com/paper/2006.04248/) (2020)
- [Statistical Learning For DC Optimal Power Flow](https://mlsanity.com/paper/1801.07809/) (2018)
- [A New Computationally Simple Approach for Implementing Neural Networks with Output Hard Constraints](https://mlsanity.com/paper/2307.10459/) (2023)
- [Co-Design Optimisation of Morphing Topology and Control of Winged Drones](https://mlsanity.com/paper/2309.13948/) (2023)
- [Efficient Primal Heuristics for Mixed Binary Quadratic Programs Using Suboptimal Rounding Guidance](https://mlsanity.com/paper/2501.05052/) (2025)
- [Efficient Evolutionary Algorithm for Single-Objective Bilevel Optimization](https://mlsanity.com/paper/1303.3901/) (2013)
- [Constraint-Handling Techniques for Particle Swarm Optimization Algorithms](https://mlsanity.com/paper/2101.10933/) (2021)
- [Perturbed Gradient Descent via Convex Quadratic Approximation for Nonconvex Bilevel Optimization](https://mlsanity.com/paper/2504.17215/) (2025)

## 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.