Adaptive, Robust and Scalable Bayesian Filtering for Online Learning
This work provides a principled framework for online learning, addressing key challenges for researchers and practitioners in machine learning, though it appears incremental as it builds on existing Bayesian filtering methods.
The thesis tackled sequential machine learning problems like online learning and contextual bandits by developing a Bayesian filtering framework to address adaptivity, robustness, and scalability, resulting in improved performance in dynamic, high-dimensional, and misspecified models as shown in theoretical and empirical results.
In this thesis, we introduce Bayesian filtering as a principled framework for tackling diverse sequential machine learning problems, including online (continual) learning, prequential (one-step-ahead) forecasting, and contextual bandits. To this end, this thesis addresses key challenges in applying Bayesian filtering to these problems: adaptivity to non-stationary environments, robustness to model misspecification and outliers, and scalability to the high-dimensional parameter space of deep neural networks. We develop novel tools within the Bayesian filtering framework to address each of these challenges, including: (i) a modular framework that enables the development adaptive approaches for online learning; (ii) a novel, provably robust filter with similar computational cost to standard filters, that employs Generalised Bayes; and (iii) a set of tools for sequentially updating model parameters using approximate second-order optimisation methods that exploit the overparametrisation of high-dimensional parametric models such as neural networks. Theoretical analysis and empirical results demonstrate the improved performance of our methods in dynamic, high-dimensional, and misspecified models.