Transfer Learning for Benign Overfitting in High-Dimensional Linear Regression

• URL: http://arxiv.org/abs/2510.15337v1
• Date: Fri, 17 Oct 2025 05:58:16 GMT
• Title: Transfer Learning for Benign Overfitting in High-Dimensional Linear Regression
• Authors: Yeichan Kim, Ilmun Kim, Seyoung Park,
• Abstract summary: We study the intersection of transfer learning and minimum-$ell$-norm interpolator (MNI) in high-dimensional linear regression.<n>Our research bridges the gap by proposing a novel two-step Transfer MNI approach and analyzing its trade-offs.
• Score: 7.414126402359073
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Transfer learning is a key component of modern machine learning, enhancing the performance of target tasks by leveraging diverse data sources. Simultaneously, overparameterized models such as the minimum-$\ell_2$-norm interpolator (MNI) in high-dimensional linear regression have garnered significant attention for their remarkable generalization capabilities, a property known as benign overfitting. Despite their individual importance, the intersection of transfer learning and MNI remains largely unexplored. Our research bridges this gap by proposing a novel two-step Transfer MNI approach and analyzing its trade-offs. We characterize its non-asymptotic excess risk and identify conditions under which it outperforms the target-only MNI. Our analysis reveals free-lunch covariate shift regimes, where leveraging heterogeneous data yields the benefit of knowledge transfer at limited cost. To operationalize our findings, we develop a data-driven procedure to detect informative sources and introduce an ensemble method incorporating multiple informative Transfer MNIs. Finite-sample experiments demonstrate the robustness of our methods to model and data heterogeneity, confirming their advantage.

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