Transfer learning (TL) has emerged as a powerful tool for improving estimation and prediction performance by leveraging information from related datasets, with the offset TL (O-TL) being a prevailing implementation. In this paper, we adapt the control-variates (CVS) method for TL and develop CVS-based estimators for scalar-on-function regression. These estimators rely exclusively on dataset-specific summary statistics, thereby avoiding the pooling of subject-level data and remaining applicable in privacy-restricted or decentralized settings. We establish, for the first time, a theoretical connection between O-TL and CVS-based TL, showing that these two seemingly distinct TL strategies adjust local estimators in fundamentally similar ways. We further derive convergence rates that explicitly account for the unavoidable but typically overlooked smoothing error arising from discretely observed functional predictors, and clarify how similarity among covariance functions across datasets governs the performance of TL. Numerical studies support the theoretical findings and demonstrate that the proposed methods achieve competitive estimation and prediction performance compared with existing alternatives.

翻译：迁移学习（TL）已成为一种通过利用相关数据集信息来提升估计与预测性能的强大工具，其中偏移迁移学习（O-TL）是一种主流的实现方式。本文针对迁移学习适配了控制变量（CVS）方法，并开发了基于CVS的函数标量回归估计器。这些估计器完全依赖于数据集特定的汇总统计量，从而避免了主体层面数据的汇集，并适用于隐私受限或去中心化的场景。我们首次建立了O-TL与基于CVS的迁移学习之间的理论联系，表明这两种表面上不同的迁移学习策略在本质上以极为相似的方式调整局部估计器。我们进一步推导了收敛速率，该速率明确考虑了由离散观测的函数预测变量所产生、通常被忽略但不可避免的平滑误差，并阐明了数据集间协方差函数的相似性如何主导迁移学习的性能。数值研究支持了理论发现，并证明所提出的方法相较于现有替代方案，在估计与预测性能上具有竞争力。