Solve for the Hyperparameter, Skip the Search: Kolmogorov-Optimal Scaling Laws for Spline Regression (opens in new tab)

Hyperparameter tuning almost always means search: fit the model at every value on a grid, score each by cross-validation, and keep the winner. For spline regression that search is unnecessary. The optimal resolution can be solved for in closed form, to the accuracy an exhaustive search reaches, at a fraction of the compute. Three ingredients make this possible: classical approximation theory pins the squared bias to a known power of the resolu...