Learning Fast Monomial Orders for Gr\"obner Basis Computations

The paper proposes treating the choice of monomial ordering for Gröbner basis computations as a reinforcement learning problem, using domain-informed reward signals that reflect actual computational cost. By training policies over the space of admissible orderings, the authors demonstrate that the learned strategies outperform traditional static heuristics such as GrevLex on benchmark problems from systems biology and computer vision. The resulting policies also resist simplification into interpretable models, suggesting that deep reinforcement learning captures complex geometric structure beyond conventional approaches.

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• agents
• computer-vision
• reinforcement-learning
• efficiency
• benchmarks