Online Optimisation for Online Learning and Control -- From No-Regret to Generalised Error Convergence
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.
Cite
@article{arxiv.1903.09869,
title = {Online Optimisation for Online Learning and Control -- From No-Regret to Generalised Error Convergence},
author = {Jan-P. Calliess},
journal= {arXiv preprint arXiv:1903.09869},
year = {2019}
}