Regularization default across problems

Ascertain whether setting the reproducing-kernel Hilbert space regularization parameter γ = 10^{-6} in the fast committor machine’s least-squares optimization is a generally suitable default across diverse committor estimation problems, and identify criteria or guidelines for selecting γ for new applications.

Background

The fast committor machine (FCM) optimizes kernel coefficients via a regularized least-squares loss whose RKHS term is controlled by a regularization parameter γ. The authors selected γ = 10^{-6} based on grid search in their experiments but note that this choice is not intuitively justified beyond those cases.

They explicitly state uncertainty about whether this choice generalizes, motivating a problem to determine principled default or data-driven selection strategies for γ across different systems and datasets.