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.

翻译：迁移学习作为现代机器学习的关键组成部分，通过利用多样化的数据源来提升目标任务的性能。与此同时，过参数化模型（例如高维线性回归中的最小-$\ell_2$-范数插值器）因其卓越的泛化能力而备受关注，这一特性被称为良性过拟合。尽管两者各自具有重要意义，但迁移学习与最小-$\ell_2$-范数插值器的交叉领域在很大程度上仍未得到探索。我们的研究通过提出一种新颖的两步迁移最小-$\ell_2$-范数插值器方法并分析其权衡，填补了这一空白。我们刻画了其非渐近超额风险，并确定了其优于仅使用目标数据的最小-$\ell_2$-范数插值器的条件。我们的分析揭示了“免费午餐”协变量偏移机制，其中利用异构数据能以有限成本获得知识迁移的收益。为了将我们的发现付诸实践，我们开发了一种数据驱动程序来检测信息源，并引入了一种融合多个信息性迁移最小-$\ell_2$-范数插值器的集成方法。有限样本实验证明了我们的方法对模型和数据异质性的鲁棒性，确认了其优势。