Reinforcing connectionism : learning the statistical way

Connectionism's main contribution to cognitive science will prove to be the renewed impetus it has imparted to learning. Learning can be integrated into the existing theoretical foundations of the subject, and the combination, statistical computational theories, provide a framework within which many connectionist mathematical mechanisms naturally fit. Examples from supervised and reinforcement learning demonstrate this. Statistical computational theories already exist for certain associative matrix memories. This work is extended, allowing real valued synapses and arbitrarily biased inputs. It shows that a covariance learning rule optimises the signal/noise ratio, a measure of the potential quality of the memory, and quantifies the performance penalty incurred by other rules. In particular two that have been suggested as occurring naturally are shown to be asymptotically optimal in the limit of sparse coding. The mathematical model is justified in comparison with other treatments whose results differ. Reinforcement comparison is a way of hastening the learning of reinforcement learning systems in statistical environments. Previous theoretical analysis has not distinguished between different comparison terms, even though empirically, a covariance rule has been shown to be better than just a constant one. The workings of reinforcement comparison are investigated by a second order analysis of the expected statistical performance of learning, and an alternative rule is proposed and empirically justified. The existing proof that temporal difference prediction learning converges in the mean is extended from a special case involving adjacent time steps to the general case involving arbitrary ones. The interaction between the statistical mechanism of temporal difference and the linear representation is particularly stark. The performance of the method given a linearly dependent representation is also analysed. The method of planning using temporal difference prediction had previously been applied to solve the navigation task of finding a goal in a grid. This is extended to compare the qualities of alternative representations of the environment and to accomplish simple latent learning when the goal is initially absent. Representations that are coarse-coded are shown to perform particularly well, and latent learning can be used to form them.