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Adaptive Regularization for Random Features: A Neighboring Early-Stopping Rule with Oracle-Rate Guarantees

arXiv · AI, language, vision and robotics · article · Aug 26, 2026 · UTC

Random feature methods provide a scalable approximation to kernel ridge regression (KRR), but the regularization parameter that yields the oracle learning rate depends on unknown smoothness and capacity parameters. In this work, we propose a neighboring early-stopping rule for adaptive regularization in KRR with random features (KRR-RF). The method uses a grid that is uniform in inverse regularization and compares only adjacent estimators, reducing the number of discrepancy comparisons relative to standard all-pairs Lepskii-type procedures. Both the neighboring discrepancy and its empirical co

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