  Neural networks have achieved remarkable success in many cognitive tasks.
However, when they are trained sequentially on multiple tasks without access to
old data, their performance on early tasks tend to drop significantly. This
problem is often referred to as catastrophic forgetting, a key challenge in
continual learning of neural networks. The regularization-based approach is one
of the primary classes of methods to alleviate catastrophic forgetting. In this
paper, we provide a novel viewpoint of regularization-based continual learning
by formulating it as a second-order Taylor approximation of the loss function
of each task. This viewpoint leads to a unified framework that can be
instantiated to derive many existing algorithms such as Elastic Weight
Consolidation and Kronecker factored Laplace approximation. Based on this
viewpoint, we study the optimization aspects (i.e., convergence) as well as
generalization properties (i.e., finite-sample guarantees) of
regularization-based continual learning. Our theoretical results indicate the
importance of accurate approximation of the Hessian matrix. The experimental
results on several benchmarks provide empirical validation of our theoretical
findings.
