What makes math problems hard for reinforcement learning: a case study
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arXiv
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| Auteurs principaux: | , , , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913685658664960 |
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| author | Shehper, Ali Medina-Mardones, Anibal M. Fagan, Lucas Lewandowski, Bartłomiej Gruen, Angus Qiu, Yang Kucharski, Piotr Wang, Zhenghan Gukov, Sergei |
| author_facet | Shehper, Ali Medina-Mardones, Anibal M. Fagan, Lucas Lewandowski, Bartłomiej Gruen, Angus Qiu, Yang Kucharski, Piotr Wang, Zhenghan Gukov, Sergei |
| contents | Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high rewards. Based on lessons learned in the context defined by the Andrews-Curtis conjecture, we propose algorithmic enhancements and a topological hardness measure with implications for a broad class of search problems. As part of our study, we also address several open mathematical questions. Notably, we demonstrate the length reducibility of all but two presentations in the Akbulut-Kirby series (1981), and resolve various potential counterexamples in the Miller-Schupp series (1991), including three infinite subfamilies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15332 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | What makes math problems hard for reinforcement learning: a case study Shehper, Ali Medina-Mardones, Anibal M. Fagan, Lucas Lewandowski, Bartłomiej Gruen, Angus Qiu, Yang Kucharski, Piotr Wang, Zhenghan Gukov, Sergei Machine Learning Artificial Intelligence Combinatorics Group Theory Geometric Topology Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high rewards. Based on lessons learned in the context defined by the Andrews-Curtis conjecture, we propose algorithmic enhancements and a topological hardness measure with implications for a broad class of search problems. As part of our study, we also address several open mathematical questions. Notably, we demonstrate the length reducibility of all but two presentations in the Akbulut-Kirby series (1981), and resolve various potential counterexamples in the Miller-Schupp series (1991), including three infinite subfamilies. |
| title | What makes math problems hard for reinforcement learning: a case study |
| topic | Machine Learning Artificial Intelligence Combinatorics Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2408.15332 |