Inability of a graph neural network heuristic to outperform greedy algorithms in solving combinatorial optimization problems
Autor: | Stefan Boettcher |
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Rok vydání: | 2022 |
Předmět: |
FOS: Computer and information sciences
Computer Science - Machine Learning Quantum Physics Computer Science - Artificial Intelligence Computer Networks and Communications FOS: Physical sciences Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks Machine Learning (cs.LG) Human-Computer Interaction Artificial Intelligence (cs.AI) Optimization and Control (math.OC) Artificial Intelligence FOS: Mathematics Computer Vision and Pattern Recognition Quantum Physics (quant-ph) Mathematics - Optimization and Control Software |
Zdroj: | Nature Machine Intelligence. 5:24-25 |
ISSN: | 2522-5839 |
Popis: | In Nature Machine Intelligence 4, 367 (2022), Schuetz et al provide a scheme to employ graph neural networks (GNN) as a heuristic to solve a variety of classical, NP-hard combinatorial optimization problems. It describes how the network is trained on sample instances and the resulting GNN heuristic is evaluated applying widely used techniques to determine its ability to succeed. Clearly, the idea of harnessing the powerful abilities of such networks to ``learn'' the intricacies of complex, multimodal energy landscapes in such a hands-off approach seems enticing. And based on the observed performance, the heuristic promises to be highly scalable, with a computational cost linear in the input size $n$, although there is likely a significant overhead in the pre-factor due to the GNN itself. However, closer inspection shows that the reported results for this GNN are only minutely better than those for gradient descent and get outperformed by a greedy algorithm, for example, for Max-Cut. The discussion also highlights what I believe are some common misconceptions in the evaluations of heuristics. RevTex4, 2 pages, 1 figure; comment on arXiv:2107.01188. Related information at http://www.physics.emory.edu/faculty/boettcher/ |
Databáze: | OpenAIRE |
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