  We study subsampling-based ridge ensembles in the proportional asymptotics
regime, where the feature size grows proportionally with the sample size such
that their ratio converges to a constant. By analyzing the squared prediction
risk of ridge ensembles as a function of the explicit penalty $\lambda$ and the
limiting subsample aspect ratio $\phi_s$ (the ratio of the feature size to the
subsample size), we characterize contours in the $(\lambda, \phi_s)$-plane at
any achievable risk. As a consequence, we prove that the risk of the optimal
full ridgeless ensemble (fitted on all possible subsamples) matches that of the
optimal ridge predictor. In addition, we prove strong uniform consistency of
generalized cross-validation (GCV) over the subsample sizes for estimating the
prediction risk of ridge ensembles. This allows for GCV-based tuning of full
ridgeless ensembles without sample splitting and yields a predictor whose risk
matches optimal ridge risk.
