Hybrid dynamical systems analysis of on-line learning in a non-stationary environment

The basic problem in machine learning is to build a model from data. On-line learning refers to the situation in which learning is done in real time. Rather having a collection of data at the start of learning, data acquisition and learning are done simultaneously. This is relevant for embedded learning systems, for example. If the data is generated by a process which is unchanging in time, many learning algorithms can be used and there is good understanding of their behaviour. In many cases, however, the underlying system is changing in time, and it may not be changing gradually, but may undergo abrupt changes. This is

This project is a collaboration with mathematicians to apply methods from hybrid dynamical systems to the analysis of on-line learning algorithms. Hybrid dynamical systems refers to mathematical theory of systems in which there are continuous changes and discrete changes
over time. This is relevant to the machine learning problem described above, because both the structure of the learning model and continuous parameters will need to change during learning in a changing environment. The goal of this research is to explore the extent to which this mathematical theory can be used to analyse and construct learning algorithms. The hypothesis is that such analysis can be used to optimise learning rates.