  Many sequential decision-making problems that are currently automated, such
as those in manufacturing or recommender systems, operate in an environment
where there is either little uncertainty, or zero risk of catastrophe. As
companies and researchers attempt to deploy autonomous systems in less
constrained environments, it is increasingly important that we endow sequential
decision-making algorithms with the ability to reason about uncertainty and
risk.
  In this thesis, we will address both planning and reinforcement learning (RL)
approaches to sequential decision-making. In the planning setting, it is
assumed that a model of the environment is provided, and a policy is optimised
within that model. Reinforcement learning relies upon extensive random
exploration, and therefore usually requires a simulator in which to perform
training. In many real-world domains, it is impossible to construct a perfectly
accurate model or simulator. Therefore, the performance of any policy is
inevitably uncertain due to the incomplete knowledge about the environment.
Furthermore, in stochastic domains, the outcome of any given run is also
uncertain due to the inherent randomness of the environment. These two sources
of uncertainty are usually classified as epistemic, and aleatoric uncertainty,
respectively. The over-arching goal of this thesis is to contribute to
developing algorithms that mitigate both sources of uncertainty in sequential
decision-making problems.
  We make a number of contributions towards this goal, with a focus on
model-based algorithms...
