  Some machine learning applications require continual learning - where data
comes in a sequence of datasets, each is used for training and then permanently
discarded. From a Bayesian perspective, continual learning seems
straightforward: Given the model posterior one would simply use this as the
prior for the next task. However, exact posterior evaluation is intractable
with many models, especially with Bayesian neural networks (BNNs). Instead,
posterior approximations are often sought. Unfortunately, when posterior
approximations are used, prior-focused approaches do not succeed in evaluations
designed to capture properties of realistic continual learning use cases. As an
alternative to prior-focused methods, we introduce a new approximate Bayesian
derivation of the continual learning loss. Our loss does not rely on the
posterior from earlier tasks, and instead adapts the model itself by changing
the likelihood term. We call these approaches likelihood-focused. We then
combine prior- and likelihood-focused methods into one objective, tying the two
views together under a single unifying framework of approximate Bayesian
continual learning.
