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.

翻译：迁移学习是一种新兴且流行的范式，旨在利用先前学习任务中的现有知识来提升新任务的性能。尽管其已在众多实证研究中取得成功，但迁移学习的理论分析仍然有限。在本文中，据我们所知，我们首次为迁移学习的一般过程构建了一个数学框架。我们独特的重新表述将迁移学习转化为一个优化问题，从而首次能够分析其可行性。此外，我们提出了一个新颖的“迁移风险”概念来评估迁移学习的可迁移性。使用Office-31数据集的数值研究展示了将迁移风险纳入迁移学习性能评估中的潜力和优势。