Hierarchical Reinforcement Learning for Sparse-Reward Search in Commutative Algebra

The article presents a novel hierarchical reinforcement learning (HRL) framework designed to tackle sparse-reward problems in commutative algebra, specifically addressing Kalai's algebraic Hirsch conjecture. It employs an options-based approach with an equivariant graph neural network policy, demonstrating superior performance over classical reinforcement learning methods and greedy search across various degrees. This work is significant for practitioners as it showcases the effective application of HRL in complex mathematical domains, potentially guiding future research in integrating AI with mathematical problem-solving.