Transfer learning, or domain adaptation, is concerned with machine learning problems in which training and testing data come from possibly different distributions (denoted as u and u', respectively). In this work, we give an information-theoretic analysis on the generalization error and the excess risk of transfer learning algorithms, following a line of work initiated by Russo and Zhou. Our results suggest, perhaps as expected, that the Kullback-Leibler (KL) divergence $D(u||u')$ plays an important role in characterizing the generalization error in the settings of domain adaptation. Specifically, we provide generalization error upper bounds for general transfer learning algorithms and extend the results to a specific empirical risk minimization (ERM) algorithm where data from both distributions are available in the training phase. We further apply the method to iterative, noisy gradient descent algorithms, and obtain upper bounds which can be easily calculated, only using parameters from the learning algorithms. A few illustrative examples are provided to demonstrate the usefulness of the results. In particular, our bound is tighter in specific classification problems than the bound derived using Rademacher complexity.

本文研究了迁移学习中的广义化误差和 excess risk 问题，提出了一种信息论分析方法。结果表明 Kullback-Leibler divergence 在特定环境中能很好地描述广义化误差，我们还将结果推广到一种特定的经验风险最小化算法中。同时，该方法在迭代，噪声梯度下降算法中有潜在的应用。

迁移学习的信息论分析