The goal of continual learning is to find a model that solves multiple
learning tasks which are presented sequentially to the learner. A key challenge
in this setting is that the learner may forget how to solve a previous task
when learning a new task, a phenomenon known as catastrophic forgetting. To
address this challenge, many practical methods have been proposed, including
memory-based, regularization-based, and expansion-based methods. However, a
rigorous theoretical understanding of these methods remains elusive. This paper
aims to bridge this gap between theory and practice by proposing a new
continual learning framework called Ideal Continual Learner (ICL), which is
guaranteed to avoid catastrophic forgetting by construction. We show that ICL
unifies multiple well-established continual learning methods and gives new
theoretical insights into the strengths and weaknesses of these methods. We
also derive generalization bounds for ICL which allow us to theoretically
quantify how rehearsal affects generalization. Finally, we connect ICL to
several classic subjects and research topics of modern interest, which allows
us to make historical remarks and inspire future directions.

本文提出了一个新的永续学习框架 “理想永续学习器”(ICL)，其通过构造保证避免了灾难性遗忘。我们证明了 ICL 统一了多种现有的永续学习方法，并为这些方法的优缺点提供了新的理论见解。最后，我们将 ICL 与现代研究领域中的经典主题和研究课题联系起来，以期激发未来的研究方向。