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We compute precise asymptotic expressions for the learning curves of leastsquares random feature (RF) models with either a separable strongly convexregularization or the $\ell_1$ regularization. We propose a novel multi-levelapplication of the convex Gaussian min max theorem (CGMT) to overcome thetraditional difficulty of finding computable expressions for random featuresmodels with correlated data. Our result takes the form of a computable4-dimensional scalar optimization. In contrast to previous results, ourapproach does not require solving an often intractable proximal operator, whichscales with the number of model parameters. Furthermore, we extend theuniversality results for the training and generalization errors for RF modelsto $\ell_1$ regularization. In particular, we demonstrate that under mildconditions, random feature models with elastic net or $\ell_1$ regularizationare asymptotically equivalent to a surrogate Gaussian model with the same firstand second moments. We numerically demonstrate the predictive capacity of ourresults, and show experimentally that the predicted test error is accurate evenin the non-asymptotic regime.

Random Features Model with General Convex Regularization: A Fine Grained Analysis with Precise Asymptotic Learning Curves