Adaptive Composite Online Optimization: Predictions in Static and Dynamic Environments

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Abstract

In the past few years, online convex optimization (OCO) has received notable attention in the control literature thanks to its flexible real-time nature and powerful performance guarantees. In this article, we propose new step-size rules and OCO algorithms that simultaneously exploit gradient predictions, function predictions and dynamics, features particularly pertinent to control applications. The proposed algorithms enjoy static and dynamic regret bounds in terms of the dynamics of the reference action sequence, gradient prediction error, and function prediction error, which are generalizations of known regularity measures from the literature. We present results for both convex and strongly convex costs. We validate the performance of the proposed algorithms in a trajectory tracking case study, as well as portfolio optimization using real-world datasets.

Original languageEnglish
Pages (from-to)2906-2921
JournalIEEE Transactions on Automatic Control
Volume68
Issue number5
DOIs
Publication statusPublished - 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

  • composite costs
  • Convex functions
  • Costs
  • dynamic environments
  • Heuristic algorithms
  • Mirrors
  • Online convex optimization
  • Prediction algorithms
  • predictions
  • Predictive models
  • real-time control
  • Standards

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