Robust Transfer Learning Based on Minimax Principle

The similarity between target and source tasks is a crucial quantity for theoretical analyses and algorithm designs in transfer learning studies. However, this quantity is often difficult to be precisely captured. To address this issue, we make a boundedness assumption on the task similarity and then propose a mathematical framework based on the minimax principle, which minimizes the worst-case expected population risk under this assumption. Furthermore, our proposed minimax problem can be solved analytically, which provides a guideline for designing robust transfer learning models. According to the analytical expression, we interpret the influences of sample sizes, task distances, and the model dimensionality in knowledge transferring. Then, practical algorithms are developed based on the theoretical results. Finally, experiments conducted on image classification tasks show that our approaches can achieve robust and competitive accuracies under random selections of training sets.