Smoothness Adaptive Hypothesis Transfer Learning

TL;DR

This paper introduces SATL, a kernel ridge regression-based transfer learning method that adaptively handles unknown smoothness levels in source and target functions, achieving near-optimal convergence rates.

Contribution

Proposes SATL, an adaptive transfer learning algorithm that adjusts to unknown smoothness, with theoretical guarantees matching minimax lower bounds.

Findings

SATL achieves near-minimax optimal convergence rates.

Theoretical analysis confirms the adaptivity and optimality of SATL.

Experiments support the theoretical results and demonstrate effectiveness.

Abstract

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.