I just know about the three continual learning scenarios: task incremental, class incremental, and domain incremental.

I just wonder if anyone thinks that this classification lacks rigorous theoretical support? I believe that the real-world situations are more complex than the three scenarios, and as such, they are not comprehensive.

Also I noticed that the data distribution P(X) between different tasks is different in all three scenarios. But the data distribution P(X) refers to the marginal probability distribution. Continual learning is to solve the situation of non-stationary data distribution, so why the data distribution here means the marginal probability distribution rather than joint probability distribution P(X,Y)?

For the first part of your question: TI, CI, and DI are the most common types of scenarios, but they are not the only types. Some works focus on scenarios where both new classes and instances appear in each experience such as NIC/CIR which span a wide range of scenarios.

As for the distribution changes, changing P(X) would result in changing P(X, Y) since P(X, Y) = P(Y|X).P(X). In both cases of Data Drift (changing P(X)) and Concept Drift (changing P(Y|X)), the joint distribution changes in the end.

Can P(X) and P(Y|X) change at the same time? Iâ€™m not aware of any work on that but would make sense for more realistic scenarios.

Yes, I also noticed that there are some other scenarios apart from the three most common ones, like task-agnostic continual learning, online continual learning, etc. I also looked into the data drift and concept drift. I think they are highly relevant to continual learning scenarios. I guess maybe we can extract more complicated continual learning scenarios from this perspective with formalizations.

Here we define the three scenarios that you mention based on how the aspect of the data that changes over time (i.e., the non-stationary aspect) relates to the mapping to be learned. Defined this way, for a supervised learning problem, there are only three possible scenarios, corresponding to task-, domain- and class-incremental learning.

Itâ€™s possible that there are multiple aspects of the data that change over time (and each could correspond to a different scenario), and this way more complex continual learning problems can be constructed, but those are then combinations or mixtures of these three scenarios.

These three scenarios also only describe one â€śaxisâ€ť in which continual learning problems can differ from each other. There are other, often complementary axes in which continual learning problems can differ. For example, continual learning problems can also differ in whether they are â€śtask-basedâ€ť (i.e., with sharp boundaries between different contexts) or â€śtask-freeâ€ť; this is discussed a bit in Supplementary Note 2 of the above article.