Finding Increasingly Large Extremal Graphs with AlphaZero and Tabu Search
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arXiv
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| Autori principali: | , , , , , , , , , , , , , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911970004828160 |
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| author | Mehrabian, Abbas Anand, Ankit Kim, Hyunjik Sonnerat, Nicolas Balog, Matej Comanici, Gheorghe Berariu, Tudor Lee, Andrew Ruoss, Anian Bulanova, Anna Toyama, Daniel Blackwell, Sam Paredes, Bernardino Romera Veličković, Petar Orseau, Laurent Lee, Joonkyung Naredla, Anurag Murty Precup, Doina Wagner, Adam Zsolt |
| author_facet | Mehrabian, Abbas Anand, Ankit Kim, Hyunjik Sonnerat, Nicolas Balog, Matej Comanici, Gheorghe Berariu, Tudor Lee, Andrew Ruoss, Anian Bulanova, Anna Toyama, Daniel Blackwell, Sam Paredes, Bernardino Romera Veličković, Petar Orseau, Laurent Lee, Joonkyung Naredla, Anurag Murty Precup, Doina Wagner, Adam Zsolt |
| contents | This work studies a central extremal graph theory problem inspired by a 1975 conjecture of Erdős, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this problem as a sequential decision-making problem and compare AlphaZero, a neural network-guided tree search, with tabu search, a heuristic local search method. Using either method, by introducing a curriculum -- jump-starting the search for larger graphs using good graphs found at smaller sizes -- we improve the state-of-the-art lower bounds for several sizes. We also propose a flexible graph-generation environment and a permutation-invariant network architecture for learning to search in the space of graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03583 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finding Increasingly Large Extremal Graphs with AlphaZero and Tabu Search Mehrabian, Abbas Anand, Ankit Kim, Hyunjik Sonnerat, Nicolas Balog, Matej Comanici, Gheorghe Berariu, Tudor Lee, Andrew Ruoss, Anian Bulanova, Anna Toyama, Daniel Blackwell, Sam Paredes, Bernardino Romera Veličković, Petar Orseau, Laurent Lee, Joonkyung Naredla, Anurag Murty Precup, Doina Wagner, Adam Zsolt Artificial Intelligence Discrete Mathematics Machine Learning This work studies a central extremal graph theory problem inspired by a 1975 conjecture of Erdős, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this problem as a sequential decision-making problem and compare AlphaZero, a neural network-guided tree search, with tabu search, a heuristic local search method. Using either method, by introducing a curriculum -- jump-starting the search for larger graphs using good graphs found at smaller sizes -- we improve the state-of-the-art lower bounds for several sizes. We also propose a flexible graph-generation environment and a permutation-invariant network architecture for learning to search in the space of graphs. |
| title | Finding Increasingly Large Extremal Graphs with AlphaZero and Tabu Search |
| topic | Artificial Intelligence Discrete Mathematics Machine Learning |
| url | https://arxiv.org/abs/2311.03583 |