Continual learning is an online paradigm where a learner continually accumulates knowledge from different tasks encountered over sequential time steps. Importantly, the learner is required to extend and update its knowledge without forgetting about the learning experience acquired from the past, and while avoiding the need to retrain from scratch. Given its sequential nature and its resemblance to the way humans think, continual learning offers an opportunity to address several challenges which currently stand in the way of widening the range of applicability of deep models to further real-world problems. The continual need to update the learner with data arriving sequentially strikes inherent congruence between continual learning and Bayesian inference which provides a principal platform to keep updating the prior beliefs of a model given new data, without completely forgetting the knowledge acquired from the old data. This survey inspects different settings of Bayesian continual learning, namely task-incremental learning and class-incremental learning. We begin by discussing definitions of continual learning along with its Bayesian setting, as well as the links with related fields, such as domain adaptation, transfer learning and meta-learning. Afterwards, we introduce a taxonomy offering a comprehensive categorization of algorithms belonging to the Bayesian continual learning paradigm. Meanwhile, we analyze the state-of-the-art while zooming in on some of the most prominent Bayesian continual learning algorithms to date. Furthermore, we shed some light on links between continual learning and developmental psychology, and correspondingly introduce analogies between both fields. We follow that with a discussion of current challenges, and finally conclude with potential areas for future research on Bayesian continual learning.

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