We analyze continual learning on a sequence of separable linear classification tasks with binary labels. We show theoretically that learning with weak regularization reduces to solving a sequential max-margin problem, corresponding to a special case of the Projection Onto Convex Sets (POCS) framework. We then develop upper bounds on the forgetting and other quantities of interest under various settings with recurring tasks, including cyclic and random orderings of tasks. We discuss several practical implications to popular training practices like regularization scheduling and weighting. We point out several theoretical differences between our continual classification setting and a recently studied continual regression setting.

本研究分析了具有二元标签的可分线性分类任务序列的持续学习，并理论上表明，使用弱正则化的学习将归结为解决顺序最大间隔问题，对应于凸集投影（POCS）框架的特殊情况。然后，我们在包括周期和随机任务排序在内的各种设置下开发了关于遗忘和其他感兴趣量的上限。我们讨论了对流行的训练实践（如正则化调度和加权）的几个实际影响，并指出了我们的持续分类设置与最近研究的持续回归设置之间的几个理论差异。

线性分类中可分数据的连续学习