We show that some basic moduli of continuity $\delta$ -- which measure how fast target risk decreases as source risk decreases -- appear to be at the root of many of the classical relatedness measures in transfer learning and related literature. Namely, bounds in terms of $\delta$ recover many of the existing bounds in terms of other measures of relatedness -- both in regression and classification -- and can at times be tighter. We are particularly interested in general situations where the learner has access to both source data and some or no target data. The unified perspective allowed by the moduli $\delta$ allow us to extend many existing notions of relatedness at once to these scenarios involving target data: interestingly, while $\delta$ itself might not be efficiently estimated, adaptive procedures exist -- based on reductions to confidence sets -- which can get nearly tight rates in terms of $\delta$ with no prior distributional knowledge. Such adaptivity to unknown $\delta$ immediately implies adaptivity to many classical relatedness notions, in terms of combined source and target samples' sizes.

本研究解决了迁移学习中关于从源风险到目标风险下降速度的基本连续性模量$\delta$的理解缺口。通过引入$\delta$，我们提出了一种统一的视角，扩展了现有相关性度量，并展示了自适应程序可以在缺乏先前分布知识的情况下有效估计，进而提高迁移学习的有效性和准确性。

更统一的迁移学习理论