Effectiveness of the reinforcement learning approach in higher dimensions

Investigate whether the reinforcement learning framework based on the Saito functional remains effective for constructing free hyperplane arrangements in higher projective dimensions P^r with r ≥ 3.

Background

The authors outline how their semicontinuous Saito functional and alternating least squares optimization extend in principle to hyperplane arrangements in higher-dimensional projective spaces, where Saito’s criterion involves a larger multilinear determinant and higher computational complexity.

They note that while the combinatorial tests and functional extend conceptually, the practical viability of the reinforcement learning search in these larger spaces is uncertain, motivating an explicit open question about its effectiveness beyond the plane case.