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Regret-optimal measurement-feedback control

Goel, Gautam and Hassibi, Babak (2021) Regret-optimal measurement-feedback control. Proceedings of Machine Learning Research, 144 . pp. 1270-1280. ISSN 1938-7228. https://resolver.caltech.edu/CaltechAUTHORS:20210719-210216911

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Abstract

We consider measurement-feedback control in linear dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing an online controller which competes with the optimal dynamic sequence of control actions selected in hindsight, instead of the best controller in some specific class of controllers. This formulation of regret is attractive when the environment changes over time and no single controller achieves good performance over the entire time horizon. We show that in the measurement-feedback setting, unlike in the full-information setting, there is no single online controller which outperforms every other online controller on every disturbance, and propose a new H₂-optimal online controller as a benchmark for the online controller to compete against. We show that the corresponding regret-optimal online controller can be found via a novel reduction to the classical Nehari problem from robust control and present a tight data-dependent bound on its regret.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://proceedings.mlr.press/v144/goel21a.htmlPublisherArticle
http://arxiv.org/abs/2011.12785arXivDiscussion Paper
Additional Information:© 2021 G. Goel & B. Hassibi.
Subject Keywords:dynamic regret, Nehari problem, robust control
Record Number:CaltechAUTHORS:20210719-210216911
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210719-210216911
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109930
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:20 Jul 2021 17:59
Last Modified:20 Jul 2021 17:59

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