论文标题
在布赫伯格的算法中学习选择策略
Learning selection strategies in Buchberger's algorithm
论文作者
论文摘要
研究多项式方程系统的一组精确解，很大程度上取决于单个迭代算法，即布赫伯格的算法。该算法的优化版本对于许多计算机代数系统（例如Mathematica，Maple，Sage）至关重要。我们为Buchberger的算法介绍了一种新方法，该算法使用强化学习剂执行S-PAIR选择，这是该算法的关键步骤。然后，我们研究问题的难度如何取决于域的选择和多项式分布的选择，而多项式的分布知之甚少。最后，我们使用近端策略优化（PPO）培训一个政策模型，以了解二项式方程式随机系统的S对选择策略。在某些领域，受过训练的模型在执行多项式添加的总数中优于最先进的选择启发式方法，这提供了一种概念验证，即机器学习的最新发展具有提高符号计算中算法的性能的潜力。
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.
