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arXiv 2005.01917cs.LGcs.SCmath.ACmath.AGstat.ML
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Buchberger算法中的学习选择策略

Learning selection strategies in Buchberger's algorithm

Cornell University(康奈尔大学)

Dylan Peifer, Michael Stillman, Daniel Halpern-Leistner

摘要:

研究一组多项式方程组的精确解在很大程度上依赖于一个单一的迭代算法,称为Buchberger算法。该算法的优化版本对于许多计算机代数系统(例如,Mathematica、Maple、Sage)。我们介绍了一种新的方法,Buchberger的算法,使用强化学习代理执行S-对选择,在算法中的关键步骤。然后,我们研究如何困难的问题取决于域的选择和分布的多项式,其中知之甚少。最后,我们使用近端策略优化(PPO)来训练策略模型,以学习随机二项式方程组的S-对选择策略。在某些领域中,训练模型在执行的多项式加法的总数方面优于最先进的选择算法,这提供了一个概念证明,即机器学习的最新发展有可能提高符号计算中算法的性能。

英文摘要:

Studying the set of exact solutions of a system of polynomial equations largely depends on a single iterative algorithm, known as Buchberger's algorithm. Optimized versions of this algorithm are crucial for many computer algebra systems (e.g., Mathematica, Maple, Sage). We introduce a new approach to Buchberger's algorithm that uses reinforcement learning agents to perform S-pair selection, a key step in the algorithm. We then study how the difficulty of the problem depends on the choices of domain and distribution of polynomials, about which little is known. Finally, we train a policy model using proximal policy optimization (PPO) 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 algorithms in symbolic computation.

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