  This paper studies the challenging continual learning (CL) setting of Class
Incremental Learning (CIL). CIL learns a sequence of tasks consisting of
disjoint sets of concepts or classes. At any time, a single model is built that
can be applied to predict/classify test instances of any classes learned thus
far without providing any task related information for each test instance.
Although many techniques have been proposed for CIL, they are mostly empirical.
It has been shown recently that a strong CIL system needs a strong within-task
prediction (WP) and a strong out-of-distribution (OOD) detection for each task.
However, it is still not known whether CIL is actually learnable. This paper
shows that CIL is learnable. Based on the theory, a new CIL algorithm is also
proposed. Experimental results demonstrate its effectiveness.
