Transfer Learning in Nonparametric Regression with Deep ReLU Networks

This paper develops a general transfer learning framework for nonparametric regression with data consisting of multiple groups. Under the assumption that groups share a common structure along with group-specific deviations in additive form, the proposed method employs a two-stage offset learning procedure: the first stage pools data from all groups to estimate an overall mean function, and the second stage estimates offsets for each group, yielding final group-level estimators through additive combination. Upper bounds on the $\mathcal L_2$ error are established for the proposed framework, covering a broad class of nonparametric estimators under mild complexity and noise conditions. When instantiated with deep ReLU networks, explicit convergence rates are derived under hierarchical composition models, demonstrating the ability to overcome the curse of dimensionality. Conditions that enable positive transfer with faster rates are considered, including learning with simpler functions and data augmentation through pooling samples across groups. Various simulations and real-data experiments further validate the effectiveness of the proposed method.

Many prediction problems use data from several related groups, such as different populations or demographic categories. These groups often share useful patterns, but they can also differ in important ways. A model that combines all groups may overlook these differences, while a model trained separately for each group may waste information from other related groups. This paper proposes a two-step method to address this challenge. First, the method learns a general pattern using data from all groups together. Then, it learns a separate adjustment for each group, so that predictions can reflect both shared information and group-specific behavior. This approach can be especially helpful when some groups have limited data but are related to groups with more data. We study when sharing information across groups should improve prediction, and we show how the method can be used with modern neural networks for complex data. In simulations and real-data studies, the proposed method often gives more accurate predictions than either fully pooling all groups or training each group separately.