Learning to Solve Constrained Bilevel Control Co-Design Problems

James Kotary, Himanshu Sharma, Ethan King, Draguna L Vrabie, Ferdinando Fioretto, Jan Drgona
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:222-241, 2026.

Abstract

We propose a learning to optimize (L2O) method for solving constrained parametric bilevel problems that arise in control co-design, where upper-level design variables are coupled with lower-level optimal control through explicit coupling constraints. Our self-supervised framework comprises: (i) a differentiable optimization layer to enforce lower-level optimality, and (ii) a differentiable gradient-based projection routine that iteratively reduces coupling-constraint violation while maintaining feasibility of upper-level constraints. A soft penalty is used during training to initialize predictions near feasibility, enabling stable end-to-end learning. On bilevel QPs with certified optima, our learned models achieve 10-2 relative optimality gaps while running $\tilde$ 102$\times$ faster than a mixed-integer programming (MIP) reformulation. On two optimal control co-design tasks, our approach yields 15–19% lower design cost and $\tilde$ 104$\times$ faster inference than a particle swarm optimization (PSO) baseline, while maintaining comparable constraint satisfaction. These results indicate that the proposed L2O method can deliver real-time, high-quality approximations for challenging bilevel programming problems that are computationally prohibitive using conventional methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-kotary26a, title = {Learning to Solve Constrained Bilevel Control Co-Design Problems}, author = {Kotary, James and Sharma, Himanshu and King, Ethan and Vrabie, Draguna L and Fioretto, Ferdinando and Drgona, Jan}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {222--241}, year = {2026}, editor = {Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, volume = {331}, series = {Proceedings of Machine Learning Research}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v331/main/assets/kotary26a/kotary26a.pdf}, url = {https://proceedings.mlr.press/v331/kotary26a.html}, abstract = {We propose a learning to optimize (L2O) method for solving constrained parametric bilevel problems that arise in control co-design, where upper-level design variables are coupled with lower-level optimal control through explicit coupling constraints. Our self-supervised framework comprises: (i) a differentiable optimization layer to enforce lower-level optimality, and (ii) a differentiable gradient-based projection routine that iteratively reduces coupling-constraint violation while maintaining feasibility of upper-level constraints. A soft penalty is used during training to initialize predictions near feasibility, enabling stable end-to-end learning. On bilevel QPs with certified optima, our learned models achieve 10-2 relative optimality gaps while running $\tilde$ 102$\times$ faster than a mixed-integer programming (MIP) reformulation. On two optimal control co-design tasks, our approach yields 15–19% lower design cost and $\tilde$ 104$\times$ faster inference than a particle swarm optimization (PSO) baseline, while maintaining comparable constraint satisfaction. These results indicate that the proposed L2O method can deliver real-time, high-quality approximations for challenging bilevel programming problems that are computationally prohibitive using conventional methods.} }
Endnote
%0 Conference Paper %T Learning to Solve Constrained Bilevel Control Co-Design Problems %A James Kotary %A Himanshu Sharma %A Ethan King %A Draguna L Vrabie %A Ferdinando Fioretto %A Jan Drgona %B Proceedings of The 8th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2026 %E Gaurav Sukhatme %E Lars Lindemann %E Stephen Tu %E Adam Wierman %E Nikolay Atanasov %F pmlr-v331-kotary26a %I PMLR %P 222--241 %U https://proceedings.mlr.press/v331/kotary26a.html %V 331 %X We propose a learning to optimize (L2O) method for solving constrained parametric bilevel problems that arise in control co-design, where upper-level design variables are coupled with lower-level optimal control through explicit coupling constraints. Our self-supervised framework comprises: (i) a differentiable optimization layer to enforce lower-level optimality, and (ii) a differentiable gradient-based projection routine that iteratively reduces coupling-constraint violation while maintaining feasibility of upper-level constraints. A soft penalty is used during training to initialize predictions near feasibility, enabling stable end-to-end learning. On bilevel QPs with certified optima, our learned models achieve 10-2 relative optimality gaps while running $\tilde$ 102$\times$ faster than a mixed-integer programming (MIP) reformulation. On two optimal control co-design tasks, our approach yields 15–19% lower design cost and $\tilde$ 104$\times$ faster inference than a particle swarm optimization (PSO) baseline, while maintaining comparable constraint satisfaction. These results indicate that the proposed L2O method can deliver real-time, high-quality approximations for challenging bilevel programming problems that are computationally prohibitive using conventional methods.
APA
Kotary, J., Sharma, H., King, E., Vrabie, D.L., Fioretto, F. & Drgona, J.. (2026). Learning to Solve Constrained Bilevel Control Co-Design Problems. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:222-241 Available from https://proceedings.mlr.press/v331/kotary26a.html.

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