We further corroborate our theoretical finding with various experiments.

We further corroborate our theoretical finding with various experiments.

I think the transfer distance can be interpreted as a measure of transferability, and the transfer distance defined in the paper seems to suggest that transfer learning is possible only when W_S and W_T are close to each other under the \Sigma_T norm. I understand that this definition is motivated from the proposition 1, but it is not always the case how people apply transfer learning in practice. In over-parametrized neural networks, two very different weights could both generate good performance model, but some learned features mappings can still be transferred to various tasks. Thus, I believe the transfer distance defined here does not fully characterize the transferability people discussed in general. Since the lower bound is not just characterizing the rate of the convergence, I would like to see the phase transition behavior of the bound between different regimes, and discontinuity would suggest that the lower bound is not tight at these points.

Curriculum learning (CL) is a commonly used machine learning training strategy. However, we still lack a clear theoretical understanding of CL's benefits. In this paper, we study the benefits of CL in the multitask linear regression problem under both structured and unstructured settings. For both settings, we derive the minimax rates for CL with the oracle that provides the optimal curriculum and without the oracle, where the agent has to adaptively learn a good curriculum. Our results reveal that adaptive learning can be fundamentally harder than the oracle learning in the unstructured setting, but it merely introduces a small extra term in the structured setting. To connect theory with practice, we provide justification for a popular empirical method that selects tasks with highest local prediction gain by comparing its guarantees with the minimax rates mentioned above.

Classical machine learning approaches are sensitive to non-stationarity. Transfer learning can address non-stationarity by sharing knowledge from one system to another, however, in areas like machine prognostics and defense, data is fundamentally limited. Therefore, transfer learning algorithms have little, if any, examples from which to learn. Herein, we suggest that these constraints on algorithmic learning can be addressed by systems engineering. We formally define transfer distance in general terms and demonstrate its use in empirically quantifying the transferability of models. We consider the use of transfer distance in the design of machine rebuild procedures to allow for transferable prognostic models. We also consider the use of transfer distance in predicting operational performance in computer vision. Practitioners can use the presented methodology to design and operate systems with consideration for the learning theoretic challenges faced by component learning systems.

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.

Case-based reasoning (CBR) is a problem-solving process in which a new problem is solved by retrieving a similar situation and reusing its solution. Transfer learning occurs when, after gaining experience from learning how to solve source problems, the same learner exploits this experience to improve performance and/or learning on target problems. In transfer learning, the differences between the source and target problems characterize the transfer distance. CBR can support transfer learning methods in multiple ways. We illustrate how CBR and transfer learning interact and characterize three approaches for using CBR in transfer learning: (1) as a transfer learning method, (2) for problem learning, and (3) to transfer knowledge between sets of problems. We describe examples of these approaches from our own and related work and discuss applicable transfer distances for each. We close with conclusions and directions for future research applying CBR to transfer learning.