Learning is a process wherein a learning agent enhances its performance through exposure of experience or data. Throughout this journey, the agent may encounter diverse learning environments. For example, data may be presented to the leaner all at once, in multiple batches, or sequentially. Furthermore, the distribution of each data sample could be either identical and independent (iid) or non-iid. Additionally, there may exist computational and space constraints for the deployment of the learning algorithms. The complexity of a learning task can vary significantly, depending on the learning setup and the constraints imposed upon it. However, it is worth noting that the current literature lacks formal definitions for many of the in-distribution and out-of-distribution learning paradigms. Establishing proper and universally agreed-upon definitions for these learning setups is essential for thoroughly exploring the evolution of ideas across different learning scenarios and deriving generalized mathematical bounds for these learners. In this paper, we aim to address this issue by proposing a chronological approach to defining different learning tasks using the provably approximately correct (PAC) learning framework. We will start with in-distribution learning and progress to recently proposed lifelong or continual learning. We employ consistent terminology and notation to demonstrate how each of these learning frameworks represents a specific instance of a broader, more generalized concept of learnability. Our hope is that this work will inspire a universally agreed-upon approach to quantifying different types of learning, fostering greater understanding and progress in the field.

翻译：学习是智能体通过接触经验或数据来提升其性能的过程。在这一过程中，智能体可能面临多样化的学习环境。例如，数据可能一次性、分批或顺序地呈现给学习者。此外，每个数据样本的分布可能是独立同分布（iid）或非独立同分布的。同时，学习算法的部署可能受到计算和存储空间的限制。学习任务的复杂性会因学习设置及其所受约束的不同而产生显著差异。然而值得注意的是，现有文献对许多分布内与分布外学习范式缺乏正式的定义。为这些学习设置建立恰当且普遍认可的定义，对于深入探索不同学习场景下思想的演进以及推导这些学习器的广义数学界限至关重要。本文旨在通过提出一种基于时序的方法，利用可证明近似正确（PAC）学习框架来定义不同的学习任务，从而解决这一问题。我们将从分布内学习出发，逐步扩展到近期提出的终身学习或持续学习。我们采用一致的术语和符号，以证明这些学习框架中的每一个都是更广义可学习性概念的一个具体实例。我们希望这项工作能够启发一种普遍认可的量化不同类型学习的方法，从而推动该领域的深入理解与发展。