In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. Important challenges in OCL are concerned with automatic adaptation to the particular non-stationary structure of the data, and with quantification of predictive uncertainty. Motivated by these challenges we introduce a probabilistic Bayesian online learning model by using a (possibly pretrained) neural representation and a state space model over the linear predictor weights. Non-stationarity over the linear predictor weights is modelled using a "parameter drift" transition density, parametrized by a coefficient that quantifies forgetting. Inference in the model is implemented with efficient Kalman filter recursions which track the posterior distribution over the linear weights, while online SGD updates over the transition dynamics coefficient allows to adapt to the non-stationarity seen in data. While the framework is developed assuming a linear Gaussian model, we also extend it to deal with classification problems and for fine-tuning the deep learning representation. In a set of experiments in multi-class classification using data sets such as CIFAR-100 and CLOC we demonstrate the predictive ability of the model and its flexibility to capture non-stationarity.

In this article, we aim at improving the prediction of expert aggregation by using the underlying properties of the models that provide expert predictions. We restrict ourselves to the case where expert predictions come from Kalman recursions, fitting state-space models. By using exponential weights, we construct different algorithms of Kalman recursions Aggregated Online (KAO) that compete with the best expert or the best convex combination of experts in a more or less adaptive way. We improve the existing results on expert aggregation literature when the experts are Kalman recursions by taking advantage of the second-order properties of the Kalman recursions. We apply our approach to Kalman recursions and extend it to the general adversarial expert setting by state-space modeling the errors of the experts. We apply these new algorithms to a real dataset of electricity consumption and show how it can improve forecast performances comparing to other exponentially weighted average procedures.