  Like generic multi-task learning, continual learning has the nature of
multi-objective optimization, and therefore faces a trade-off between the
performance of different tasks. That is, to optimize for the current task
distribution, it may need to compromise performance on some previous tasks.
This means that there exist multiple models that are Pareto-optimal at
different times, each addressing a distinct task performance trade-off.
Researchers have discussed how to train particular models to address specific
trade-off preferences. However, existing algorithms require training overheads
proportional to the number of preferences -- a large burden when there are
multiple, possibly infinitely many, preferences. As a response, we propose
Imprecise Bayesian Continual Learning (IBCL). Upon a new task, IBCL (1) updates
a knowledge base in the form of a convex hull of model parameter distributions
and (2) obtains particular models to address task trade-off preferences with
zero-shot. That is, IBCL does not require any additional training overhead to
generate preference-addressing models from its knowledge base. We show that
models obtained by IBCL have guarantees in identifying the Pareto optimal
parameters. Moreover, experiments on standard image classification and NLP
tasks support this guarantee. Statistically, IBCL improves average per-task
accuracy by at most 23\% and peak per-task accuracy by at most 15\% with
respect to the baseline methods, with steadily near-zero or positive backward
transfer. Most importantly, IBCL significantly reduces the training overhead
from training 1 model per preference to at most 3 models for all preferences.
