Summary of What Makes Math Problems Hard For Reinforcement Learning: a Case Study, by Ali Shehper et al.
What makes math problems hard for reinforcement learning: a case study
by Ali Shehper, Anibal M. Medina-Mardones, Lucas Fagan, Bartłomiej Lewandowski, Angus Gruen, Yang Qiu, Piotr Kucharski, Zhenghan Wang, Sergei Gukov
First submitted to arxiv on: 27 Aug 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Combinatorics (math.CO); Group Theory (math.GR); Geometric Topology (math.GT)
GrooveSquid.com Paper Summaries
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper delves into the challenges of finding rare instances with high rewards by leveraging a conjecture from combinatorial group theory. The authors propose algorithmic enhancements and a topological hardness measure, which have implications for various search problems. Additionally, they address several open mathematical questions, including resolving potential counterexamples in the Miller-Schupp series (1991). Specifically, they demonstrate the length reducibility of all but two presentations in the Akbulut-Kirby series (1981) and identify three infinite subfamilies. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about finding rare things that are really valuable. Imagine searching for a needle in a haystack, and you want to find the ones with big rewards. The authors use an idea from math to help solve this problem. They come up with new ways to make the search easier and create a way to measure how hard it is to find these special things. Along the way, they also answer some long-standing math questions that have puzzled experts for years. |
