Continual Learning via Dynamic Programming

Continual learning (CL) algorithms seek to train a model when faced with similar tasks observed in a sequential manner. Despite promising methodological advancements, however, there is a lack of theoretical frameworks that enable analysis of learning challenges such as generalization and catastrophic forgetting, especially in applications where the tasks are generated continuously through a partial differential equation. To address this lack, we present a new theoretical framework that models the learning dynamics in CL through dynamic programming. Using the proposed framework, we derive a new method that adopts stochastic-gradient-driven alternating optimization to balance generalization and catastrophic forgetting. We establish conditions for convergence and show that, on CL benchmark datasets, our method achieves accuracies better than or comparable to those of existing state-of-the-art methods.