A Hybrid Learning-to-Optimize Framework for Mixed-Integer Quadratic Programming

Viet-Anh Le, Mu Xie, Rahul Mangharam
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:1055-1069, 2026.

Abstract

In this paper, we propose a learning-to-optimize (L2O) framework to accelerate solving parametric mixed-integer quadratic programming (MIQP) problems, with a particular focus on mixed-integer model predictive control (MI-MPC) applications. The framework learns to predict integer solutions with enhanced optimality and feasibility by integrating supervised learning (for optimality), self-supervised learning (for feasibility), and a differentiable quadratic programming (QP) layer, resulting in a hybrid L2O framework. Specifically, a neural network (NN) is used to learn the mapping from problem parameters to optimal integer solutions, while a differentiable QP layer is integrated to compute the corresponding continuous variables given the predicted integers and problem parameters. Moreover, a hybrid loss function is proposed, which combines a supervised loss with respect to the global optimal solution, and a self-supervised loss derived from the problem’s objective and constraints. The effectiveness of the proposed framework is demonstrated on two benchmark MI-MPC problems, with comparative results against purely supervised and self-supervised learning models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-le26a, title = {A Hybrid Learning-to-Optimize Framework for Mixed-Integer Quadratic Programming}, author = {Le, Viet-Anh and Xie, Mu and Mangharam, Rahul}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {1055--1069}, 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/le26a/le26a.pdf}, url = {https://proceedings.mlr.press/v331/le26a.html}, abstract = {In this paper, we propose a learning-to-optimize (L2O) framework to accelerate solving parametric mixed-integer quadratic programming (MIQP) problems, with a particular focus on mixed-integer model predictive control (MI-MPC) applications. The framework learns to predict integer solutions with enhanced optimality and feasibility by integrating supervised learning (for optimality), self-supervised learning (for feasibility), and a differentiable quadratic programming (QP) layer, resulting in a hybrid L2O framework. Specifically, a neural network (NN) is used to learn the mapping from problem parameters to optimal integer solutions, while a differentiable QP layer is integrated to compute the corresponding continuous variables given the predicted integers and problem parameters. Moreover, a hybrid loss function is proposed, which combines a supervised loss with respect to the global optimal solution, and a self-supervised loss derived from the problem’s objective and constraints. The effectiveness of the proposed framework is demonstrated on two benchmark MI-MPC problems, with comparative results against purely supervised and self-supervised learning models.} }
Endnote
%0 Conference Paper %T A Hybrid Learning-to-Optimize Framework for Mixed-Integer Quadratic Programming %A Viet-Anh Le %A Mu Xie %A Rahul Mangharam %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-le26a %I PMLR %P 1055--1069 %U https://proceedings.mlr.press/v331/le26a.html %V 331 %X In this paper, we propose a learning-to-optimize (L2O) framework to accelerate solving parametric mixed-integer quadratic programming (MIQP) problems, with a particular focus on mixed-integer model predictive control (MI-MPC) applications. The framework learns to predict integer solutions with enhanced optimality and feasibility by integrating supervised learning (for optimality), self-supervised learning (for feasibility), and a differentiable quadratic programming (QP) layer, resulting in a hybrid L2O framework. Specifically, a neural network (NN) is used to learn the mapping from problem parameters to optimal integer solutions, while a differentiable QP layer is integrated to compute the corresponding continuous variables given the predicted integers and problem parameters. Moreover, a hybrid loss function is proposed, which combines a supervised loss with respect to the global optimal solution, and a self-supervised loss derived from the problem’s objective and constraints. The effectiveness of the proposed framework is demonstrated on two benchmark MI-MPC problems, with comparative results against purely supervised and self-supervised learning models.
APA
Le, V., Xie, M. & Mangharam, R.. (2026). A Hybrid Learning-to-Optimize Framework for Mixed-Integer Quadratic Programming. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:1055-1069 Available from https://proceedings.mlr.press/v331/le26a.html.

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