  Transfer learning is an emerging and popular paradigm for utilizing existing
knowledge from previous learning tasks to improve the performance of new ones.
Despite its numerous empirical successes, theoretical analysis for transfer
learning is limited. In this paper we build for the first time, to the best of
our knowledge, a mathematical framework for the general procedure of transfer
learning. Our unique reformulation of transfer learning as an optimization
problem allows for the first time, analysis of its feasibility. Additionally,
we propose a novel concept of transfer risk to evaluate transferability of
transfer learning. Our numerical studies using the Office-31 dataset
demonstrate the potential and benefits of incorporating transfer risk in the
evaluation of transfer learning performance.
