Many existing two-phase kernel-based hypothesis transfer learning algorithms employ the same kernel regularization across phases and rely on the known smoothness of functions to obtain optimality. Therefore, they fail to adapt to the varying and unknown smoothness between the target/source and their offset in practice. In this paper, we address these problems by proposing Smoothness Adaptive Transfer Learning (SATL), a two-phase kernel ridge regression(KRR)-based algorithm. We first prove that employing the misspecified fixed bandwidth Gaussian kernel in target-only KRR learning can achieve minimax optimality and derive an adaptive procedure to the unknown Sobolev smoothness. Leveraging these results, SATL employs Gaussian kernels in both phases so that the estimators can adapt to the unknown smoothness of the target/source and their offset function. We derive the minimax lower bound of the learning problem in excess risk and show that SATL enjoys a matching upper bound up to a logarithmic factor. The minimax convergence rate sheds light on the factors influencing transfer dynamics and demonstrates the superiority of SATL compared to non-transfer learning settings. While our main objective is a theoretical analysis, we also conduct several experiments to confirm our results.

通过提出两阶段核岭回归的 Smoothness Adaptive Transfer Learning (SATL) 算法，解决了现有两阶段基于核的假设迁移学习算法在实践中由于目标/源与偏移之间的可变和未知平滑度而适应性不足的问题，通过采用高斯核适应目标/源以及其偏移函数的未知平滑度，SATL算法能够实现最小极值优化，同时通过最小极值收敛速率揭示了影响迁移动态的因素，并证明了与非迁移学习设置相比，SATL具有更好的性能。

平滑自适应假设迁移学习