  This paper addresses challenges in robust transfer learning stemming from
ambiguity in Bayes classifiers and weak transferable signals between the target
and source distribution. We introduce a novel quantity called the ''ambiguity
level'' that measures the discrepancy between the target and source regression
functions, propose a simple transfer learning procedure, and establish a
general theorem that shows how this new quantity is related to the
transferability of learning in terms of risk improvements. Our proposed
''Transfer Around Boundary'' (TAB) model, with a threshold balancing the
performance of target and source data, is shown to be both efficient and
robust, improving classification while avoiding negative transfer. Moreover, we
demonstrate the effectiveness of the TAB model on non-parametric classification
and logistic regression tasks, achieving upper bounds which are optimal up to
logarithmic factors. Simulation studies lend further support to the
effectiveness of TAB. We also provide simple approaches to bound the excess
misclassification error without the need for specialized knowledge in transfer
learning.
