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

Jan-P. Calliess

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arXiv · 1903.09869

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

Jan-P. Calliess

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Abstract

This paper presents early work aiming at the development of a new framework for the design and analysis of algorithms for online learning based prediction and control. Firstly, we consider the task of predicting values of a function or time series based on incrementally arriving sequences of inputs by utilising online programming. Introducing a generalisation of standard notions of convergence, we derive theoretical guarantees on the asymptotic behaviour of the prediction accuracies when prediction models are updated by a no-external-regret algorithm. We prove generalised learning guarantees for online regression and provide an example of how this can be applied to online learning-based control. We devise a model-reference adaptive controller with novel online performance guarantees on tracking success in the presence of a priori dynamic uncertainty. Our theoretical results are accompanied by illustrations on simple regression and control problems.

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BibTeX RIS

Jan-P. Calliess. 2019-03-23. Online Optimisation for Online Learning and Control -- From No-Regret to Generalised Error Convergence. https://arxiv.org/abs/1903.09869

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