  Continual learning, an important aspect of artificial intelligence and
machine learning research, focuses on developing models that learn and adapt to
new tasks while retaining previously acquired knowledge. Existing continual
learning algorithms usually involve a small number of tasks with uniform sizes
and may not accurately represent real-world learning scenarios. In this paper,
we investigate the performance of continual learning algorithms with a large
number of tasks drawn from a task distribution that is long-tail in terms of
task sizes. We design one synthetic dataset and two real-world continual
learning datasets to evaluate the performance of existing algorithms in such a
setting. Moreover, we study an overlooked factor in continual learning, the
optimizer states, e.g. first and second moments in the Adam optimizer, and
investigate how it can be used to improve continual learning performance. We
propose a method that reuses the optimizer states in Adam by maintaining a
weighted average of the second moments from previous tasks. We demonstrate that
our method, compatible with most existing continual learning algorithms,
effectively reduces forgetting with only a small amount of additional
computational or memory costs, and provides further improvements on existing
continual learning algorithms, particularly in a long-tail task sequence.
