Minimax Lower Bounds for Transfer Learning with Linear and One-hidden Layer Neural Networks
This work addresses the lack of theoretical understanding of transfer learning benefits and limits for researchers and practitioners in machine learning, though it is incremental as it builds on existing minimax frameworks.
The paper tackles the problem of understanding the fundamental limits of transfer learning by developing a statistical minimax framework for regression with linear and one-hidden layer neural networks, deriving a lower bound for target generalization error based on data quantities and task similarity.
Transfer learning has emerged as a powerful technique for improving the performance of machine learning models on new domains where labeled training data may be scarce. In this approach a model trained for a source task, where plenty of labeled training data is available, is used as a starting point for training a model on a related target task with only few labeled training data. Despite recent empirical success of transfer learning approaches, the benefits and fundamental limits of transfer learning are poorly understood. In this paper we develop a statistical minimax framework to characterize the fundamental limits of transfer learning in the context of regression with linear and one-hidden layer neural network models. Specifically, we derive a lower-bound for the target generalization error achievable by any algorithm as a function of the number of labeled source and target data as well as appropriate notions of similarity between the source and target tasks. Our lower bound provides new insights into the benefits and limitations of transfer learning. We further corroborate our theoretical finding with various experiments.