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This paper presents early work aiming at the development of a new frameworkfor the design and analysis of algorithms for online learning based predictionand control. Firstly, we consider the task of predicting values of a functionor time series based on incrementally arriving sequences of inputs by utilisingonline programming. Introducing a generalisation of standard notions ofconvergence, we derive theoretical guarantees on the asymptotic behaviour ofthe prediction accuracies when prediction models are updated by ano-external-regret algorithm. We prove generalised learning guarantees foronline regression and provide an example of how this can be applied to onlinelearning-based control. We devise a model-reference adaptive controller withnovel online performance guarantees on tracking success in the presence of apriori dynamic uncertainty. Our theoretical results are accompanied byillustrations on simple regression and control problems.

Online Optimisation for Online Learning and Control -- From No-Regret to Generalised Error Convergence