Learning Selection Strategies in Buchberger's Algorithm

Speaker: Dylan Peifer, Cornell University, a visiting Ph.D. student at Illinois Tech this academic year, with an in using machine learning for computational algebra

Description:

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, such as Macaulay2, Singular, or Maple. In this work, 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. In domains consisting of random binomial ideals, models trained using standard deep reinforcement learning techniques outperform state-of-the-art human-designed selection heuristics in a total number of polynomial additions performed by 20-40%, providing a proof-of-concept that recent developments in machine learning have the potential to improve performance of algorithms in symbolic computation significantly.

Nonlinear Algebra and Statistics (NLASTATS) Seminar