Intelligent Systems
Note: This research group has relocated.

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

2021

Conference Paper

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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.

Author(s): Anselm Paulus and Michal Rolínek and Vít Musil and Brandon Amos and Georg Martius
Book Title: Proceedings of the 38th International Conference on Machine Learning
Volume: 139
Pages: 8443--8453
Year: 2021
Month: July
Day: 18--24

Series: Proceedings of Machine Learning Research
Editors: Meila, Marina and Zhang, Tong
Publisher: PMLR

Department(s): Autonomous Learning
Research Project(s): Combinatorial Optimization as a Layer / Blackbox Differentiation
Bibtex Type: Conference Paper (inproceedings)
Paper Type: Conference

Event Name: The Thirty-eighth International Conference on Machine Learning (ICML)
Event Place: Virtual

Language: English
Talk Type: Spotlight
URL: https://proceedings.mlr.press/v139/paulus21a.html

Additional (custom) Fields:
pdf: http://proceedings.mlr.press/v139/paulus21a/paulus21a.pdf

Links: Arxiv
Code
Pdf
Spotlight video @ ICML 2021
Poster @ ICML 2021

BibTex

@inproceedings{paulus2021:comboptnet,
  title = {CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints},
  author = {Paulus, Anselm and Rolínek, Michal and Musil, Vít and Amos, Brandon and Martius, Georg},
  booktitle = {Proceedings of the 38th International Conference on Machine Learning},
  volume = {139},
  pages = {8443--8453},
  series = {Proceedings of Machine Learning Research},
  editors = {Meila, Marina and Zhang, Tong},
  publisher = {PMLR},
  month = jul,
  year = {2021},
  doi = {},
  url = {https://proceedings.mlr.press/v139/paulus21a.html},
  month_numeric = {7}
}