LeNSE: Learning To Navigate Subgraph Embeddings for Large-Scale Combinatorial Optimisation

David Ireland, Giovanni Montana
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:9622-9638, 2022.

Abstract

Combinatorial Optimisation problems arise in several application domains and are often formulated in terms of graphs. Many of these problems are NP-hard, but exact solutions are not always needed. Several heuristics have been developed to provide near-optimal solutions; however, they do not typically scale well with the size of the graph. We propose a low-complexity approach for identifying a (possibly much smaller) subgraph of the original graph where the heuristics can be run in reasonable time and with a high likelihood of finding a global near-optimal solution. The core component of our approach is LeNSE, a reinforcement learning algorithm that learns how to navigate the space of possible subgraphs using an Euclidean subgraph embedding as its map. To solve CO problems, LeNSE is provided with a discriminative embedding trained using any existing heuristics using only on a small portion of the original graph. When tested on three problems (vertex cover, max-cut and influence maximisation) using real graphs with up to $10$ million edges, LeNSE identifies small subgraphs yielding solutions comparable to those found by running the heuristics on the entire graph, but at a fraction of the total run time. Code for the experiments is available in the public GitHub repo at https://github.com/davidireland3/LeNSE.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-ireland22a, title = {{L}e{NSE}: Learning To Navigate Subgraph Embeddings for Large-Scale Combinatorial Optimisation}, author = {Ireland, David and Montana, Giovanni}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {9622--9638}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/ireland22a/ireland22a.pdf}, url = {https://proceedings.mlr.press/v162/ireland22a.html}, abstract = {Combinatorial Optimisation problems arise in several application domains and are often formulated in terms of graphs. Many of these problems are NP-hard, but exact solutions are not always needed. Several heuristics have been developed to provide near-optimal solutions; however, they do not typically scale well with the size of the graph. We propose a low-complexity approach for identifying a (possibly much smaller) subgraph of the original graph where the heuristics can be run in reasonable time and with a high likelihood of finding a global near-optimal solution. The core component of our approach is LeNSE, a reinforcement learning algorithm that learns how to navigate the space of possible subgraphs using an Euclidean subgraph embedding as its map. To solve CO problems, LeNSE is provided with a discriminative embedding trained using any existing heuristics using only on a small portion of the original graph. When tested on three problems (vertex cover, max-cut and influence maximisation) using real graphs with up to $10$ million edges, LeNSE identifies small subgraphs yielding solutions comparable to those found by running the heuristics on the entire graph, but at a fraction of the total run time. Code for the experiments is available in the public GitHub repo at https://github.com/davidireland3/LeNSE.} }
Endnote
%0 Conference Paper %T LeNSE: Learning To Navigate Subgraph Embeddings for Large-Scale Combinatorial Optimisation %A David Ireland %A Giovanni Montana %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-ireland22a %I PMLR %P 9622--9638 %U https://proceedings.mlr.press/v162/ireland22a.html %V 162 %X Combinatorial Optimisation problems arise in several application domains and are often formulated in terms of graphs. Many of these problems are NP-hard, but exact solutions are not always needed. Several heuristics have been developed to provide near-optimal solutions; however, they do not typically scale well with the size of the graph. We propose a low-complexity approach for identifying a (possibly much smaller) subgraph of the original graph where the heuristics can be run in reasonable time and with a high likelihood of finding a global near-optimal solution. The core component of our approach is LeNSE, a reinforcement learning algorithm that learns how to navigate the space of possible subgraphs using an Euclidean subgraph embedding as its map. To solve CO problems, LeNSE is provided with a discriminative embedding trained using any existing heuristics using only on a small portion of the original graph. When tested on three problems (vertex cover, max-cut and influence maximisation) using real graphs with up to $10$ million edges, LeNSE identifies small subgraphs yielding solutions comparable to those found by running the heuristics on the entire graph, but at a fraction of the total run time. Code for the experiments is available in the public GitHub repo at https://github.com/davidireland3/LeNSE.
APA
Ireland, D. & Montana, G.. (2022). LeNSE: Learning To Navigate Subgraph Embeddings for Large-Scale Combinatorial Optimisation. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:9622-9638 Available from https://proceedings.mlr.press/v162/ireland22a.html.

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