Reinforcement Learning in Buchberger's Algorithm
| dc.contributor.author | Peifer, Dylan | |
| dc.contributor.chair | Stillman, Michael | |
| dc.contributor.committeeMember | Kozen, Dexter | |
| dc.contributor.committeeMember | Halpern-Leistner, Daniel S. | |
| dc.date.accessioned | 2021-09-09T17:40:57Z | |
| dc.date.available | 2021-09-09T17:40:57Z | |
| dc.date.issued | 2021-05 | |
| dc.description | 169 pages | |
| dc.description.abstract | Buchberger’s algorithm is the classical algorithm for computing a Gröbner basis, and optimized implementations are crucial for many computer algebra systems. In this thesis we introduce a new approach to Buchberger’s algorithm that uses deep reinforcement learning agents to perform S-pair selection, a key choice in the algorithm. We first study how the difficulty of the problem depends on several random distributions of polynomial ideals, about which little is known. Next, we train a policy model using proximal policy optimization to learn S-pair selection strategies for random systems of binomial equations. In certain domains the trained model outperforms state-of-the-art selection heuristics in total number of polynomial additions performed, which provides a proof-of-concept that recent developments in machine learning have the potential to improve performance of critical algorithms in symbolic computation. Finally, we apply these techniques to Bigatti’s algorithm for computing a Hilbert series, and consider extending these results with neural network value models and tree search. | |
| dc.identifier.doi | https://doi.org/10.7298/4fpv-bn09 | |
| dc.identifier.other | Peifer_cornellgrad_0058F_12500 | |
| dc.identifier.other | http://dissertations.umi.com/cornellgrad:12500 | |
| dc.identifier.uri | https://hdl.handle.net/1813/109782 | |
| dc.language.iso | en | |
| dc.subject | algebraic geometry | |
| dc.subject | commutative algebra | |
| dc.subject | computer algebra | |
| dc.subject | Groebner basis | |
| dc.subject | machine learning | |
| dc.subject | reinforcement learning | |
| dc.title | Reinforcement Learning in Buchberger's Algorithm | |
| dc.type | dissertation or thesis | |
| dcterms.license | https://hdl.handle.net/1813/59810 | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Cornell University | |
| thesis.degree.level | Doctor of Philosophy | |
| thesis.degree.name | Ph. D., Mathematics |
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