A thesis presented for the degree of Doctor of Philosophy, School of Computer Science and Applied Mathematics. University of the Witwatersrand, South Africa. 26 August 2016.In the reinforcement learning paradigm, an agent learns by interacting with its environment. At each
state, the agent receives a numerical reward. Its goal is to maximise the discounted sum of future rewards.
One way it can do this is through learning a value function; a function which maps states to the discounted
sum of future rewards. With an accurate value function and a model of the environment, the agent can
take the optimal action in each state. In practice, however, the value function is approximated, and
performance depends on the quality of the approximation. Linear function approximation is a commonly
used approximation scheme, where the value function is represented as a weighted sum of basis functions
or features. In continuous state environments, there are infinitely many such features to choose from,
introducing the new problem of feature selection. Existing algorithms such as OMP-TD are slow to
converge, scale poorly to high dimensional spaces, and have not been generalised to the online learning
case. We introduce heuristic methods for reducing the search space in high dimensions that significantly
reduce computational costs and also act as regularisers. We extend these methods and introduce feature
regularisation for incremental feature selection in the batch learning case, and show that introducing a
smoothness prior is effective with our SSOMP-TD and STOMP-TD algorithms. Finally we generalise
OMP-TD and our algorithms to the online case and evaluate them empirically.LG201
