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.