Information-theoretic analysis for transfer learning
This work provides theoretical insights for researchers in machine learning, but it is incremental as it builds on existing information-theoretic frameworks.
The authors tackled the problem of analyzing generalization error and excess risk in transfer learning by providing information-theoretic upper bounds, showing that Kullback-Leibler divergence plays a key role and achieving tighter bounds than Rademacher complexity in specific classification cases.
Transfer learning, or domain adaptation, is concerned with machine learning problems in which training and testing data come from possibly different distributions (denoted as $μ$ and $μ'$, 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 $D(mu||mu')$ 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.