CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints

Anselm Paulus, Michal Rolinek, Vit Musil, Brandon Amos, Georg Martius
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:8443-8453, 2021.

Abstract

Bridging logical and algorithmic reasoning with modern machine learning techniques is a fundamental challenge with potentially transformative impact. On the algorithmic side, many NP-hard problems can be expressed as integer programs, in which the constraints play the role of their ’combinatorial specification’. In this work, we aim to integrate integer programming solvers into neural network architectures as layers capable of learning both the cost terms and the constraints. The resulting end-to-end trainable architectures jointly extract features from raw data and solve a suitable (learned) combinatorial problem with state-of-the-art integer programming solvers. We demonstrate the potential of such layers with an extensive performance analysis on synthetic data and with a demonstration on a competitive computer vision keypoint matching benchmark.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-paulus21a, title = {CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints}, author = {Paulus, Anselm and Rolinek, Michal and Musil, Vit and Amos, Brandon and Martius, Georg}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {8443--8453}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/paulus21a/paulus21a.pdf}, url = {https://proceedings.mlr.press/v139/paulus21a.html}, abstract = {Bridging logical and algorithmic reasoning with modern machine learning techniques is a fundamental challenge with potentially transformative impact. On the algorithmic side, many NP-hard problems can be expressed as integer programs, in which the constraints play the role of their ’combinatorial specification’. In this work, we aim to integrate integer programming solvers into neural network architectures as layers capable of learning both the cost terms and the constraints. The resulting end-to-end trainable architectures jointly extract features from raw data and solve a suitable (learned) combinatorial problem with state-of-the-art integer programming solvers. We demonstrate the potential of such layers with an extensive performance analysis on synthetic data and with a demonstration on a competitive computer vision keypoint matching benchmark.} }
Endnote
%0 Conference Paper %T CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints %A Anselm Paulus %A Michal Rolinek %A Vit Musil %A Brandon Amos %A Georg Martius %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-paulus21a %I PMLR %P 8443--8453 %U https://proceedings.mlr.press/v139/paulus21a.html %V 139 %X Bridging logical and algorithmic reasoning with modern machine learning techniques is a fundamental challenge with potentially transformative impact. On the algorithmic side, many NP-hard problems can be expressed as integer programs, in which the constraints play the role of their ’combinatorial specification’. In this work, we aim to integrate integer programming solvers into neural network architectures as layers capable of learning both the cost terms and the constraints. The resulting end-to-end trainable architectures jointly extract features from raw data and solve a suitable (learned) combinatorial problem with state-of-the-art integer programming solvers. We demonstrate the potential of such layers with an extensive performance analysis on synthetic data and with a demonstration on a competitive computer vision keypoint matching benchmark.
APA
Paulus, A., Rolinek, M., Musil, V., Amos, B. & Martius, G.. (2021). CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:8443-8453 Available from https://proceedings.mlr.press/v139/paulus21a.html.

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