Can Computational Reducibility Lead to Transferable Models for Graph Combinatorial Optimization?

Semih Cantürk, Thomas Sabourin, Frederik Wenkel, Michael Perlmutter, Guy Wolf
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:11063-11082, 2026.

Abstract

A key challenge in developing unified neural solvers for combinatorial optimization (CO) is the efficient generalization of models from a given set of tasks to new tasks unseen during initial training. To address this, we first establish a new GNN encoder, which uses a GCON module as a form of expressive message passing together with energy-based unsupervised loss functions. This model achieves highly competitive performance across multiple CO tasks when trained individually on each task. We then leverage knowledge from the computational reducibility literature to propose pretraining and fine-tuning strategies that transfer effectively (a) between MVC, MIS and MaxClique, and (b) in a multi-task learning setting that additionally incorporates MaxCut, MDS and graph coloring. Additionally, in a leave-one-out, multi-task learning setting, we observe that pretraining on all but one task almost always leads to faster convergence on the remaining task when fine-tuning, while avoiding negative transfer. Our findings indicate that learning common representations across multiple graph CO problems is viable through the use of expressive message passing coupled with pretraining strategies that are informed by the polynomial reducibility literature, thereby taking an important step towards enabling the development of foundational models for neural CO. We provide an open source implementation of our work at https://github.com/semihcanturk/COPT-MT.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-canturk26a, title = {Can Computational Reducibility Lead to Transferable Models for Graph Combinatorial Optimization?}, author = {Cant\"{u}rk, Semih and Sabourin, Thomas and Wenkel, Frederik and Perlmutter, Michael and Wolf, Guy}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {11063--11082}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/canturk26a/canturk26a.pdf}, url = {https://proceedings.mlr.press/v306/canturk26a.html}, abstract = {A key challenge in developing unified neural solvers for combinatorial optimization (CO) is the efficient generalization of models from a given set of tasks to new tasks unseen during initial training. To address this, we first establish a new GNN encoder, which uses a GCON module as a form of expressive message passing together with energy-based unsupervised loss functions. This model achieves highly competitive performance across multiple CO tasks when trained individually on each task. We then leverage knowledge from the computational reducibility literature to propose pretraining and fine-tuning strategies that transfer effectively (a) between MVC, MIS and MaxClique, and (b) in a multi-task learning setting that additionally incorporates MaxCut, MDS and graph coloring. Additionally, in a leave-one-out, multi-task learning setting, we observe that pretraining on all but one task almost always leads to faster convergence on the remaining task when fine-tuning, while avoiding negative transfer. Our findings indicate that learning common representations across multiple graph CO problems is viable through the use of expressive message passing coupled with pretraining strategies that are informed by the polynomial reducibility literature, thereby taking an important step towards enabling the development of foundational models for neural CO. We provide an open source implementation of our work at https://github.com/semihcanturk/COPT-MT.} }
Endnote
%0 Conference Paper %T Can Computational Reducibility Lead to Transferable Models for Graph Combinatorial Optimization? %A Semih Cantürk %A Thomas Sabourin %A Frederik Wenkel %A Michael Perlmutter %A Guy Wolf %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-canturk26a %I PMLR %P 11063--11082 %U https://proceedings.mlr.press/v306/canturk26a.html %V 306 %X A key challenge in developing unified neural solvers for combinatorial optimization (CO) is the efficient generalization of models from a given set of tasks to new tasks unseen during initial training. To address this, we first establish a new GNN encoder, which uses a GCON module as a form of expressive message passing together with energy-based unsupervised loss functions. This model achieves highly competitive performance across multiple CO tasks when trained individually on each task. We then leverage knowledge from the computational reducibility literature to propose pretraining and fine-tuning strategies that transfer effectively (a) between MVC, MIS and MaxClique, and (b) in a multi-task learning setting that additionally incorporates MaxCut, MDS and graph coloring. Additionally, in a leave-one-out, multi-task learning setting, we observe that pretraining on all but one task almost always leads to faster convergence on the remaining task when fine-tuning, while avoiding negative transfer. Our findings indicate that learning common representations across multiple graph CO problems is viable through the use of expressive message passing coupled with pretraining strategies that are informed by the polynomial reducibility literature, thereby taking an important step towards enabling the development of foundational models for neural CO. We provide an open source implementation of our work at https://github.com/semihcanturk/COPT-MT.
APA
Cantürk, S., Sabourin, T., Wenkel, F., Perlmutter, M. & Wolf, G.. (2026). Can Computational Reducibility Lead to Transferable Models for Graph Combinatorial Optimization?. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:11063-11082 Available from https://proceedings.mlr.press/v306/canturk26a.html.

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