  Meta continual learning algorithms seek to train a model when faced with
similar tasks observed in a sequential manner. Despite promising methodological
advancements, there is a lack of theoretical frameworks that enable analysis of
learning challenges such as generalization and catastrophic forgetting. To that
end, we develop a new theoretical approach for meta continual learning~(MCL)
where we mathematically model the learning dynamics using dynamic programming,
and we establish conditions of optimality for the MCL problem. Moreover, using
the theoretical framework, we derive a new dynamic-programming-based MCL method
that adopts stochastic-gradient-driven alternating optimization to balance
generalization and catastrophic forgetting. We show that, on MCL benchmark data
sets, our theoretically grounded method achieves accuracy better than or
comparable to that of existing state-of-the-art methods.
