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Double Coverage with Machine-Learned Advice

Authors Alexander Lindermayr , Nicole Megow , Bertrand Simon

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Author Details

Alexander Lindermayr
  • Faculty of Mathematics and Computer Science, University of Bremen, Germany
Nicole Megow
  • Faculty of Mathematics and Computer Science, University of Bremen, Germany
Bertrand Simon
  • IN2P3 Computing Center, CNRS, Villeurbanne, France

Funding

Partially supported by the German Science Foundation (DFG) under contracts ME 3825/1 and 146371743 - TRR 89 Invasive Computing.

Cite AsGet BibTex

Alexander Lindermayr, Nicole Megow, and Bertrand Simon. Double Coverage with Machine-Learned Advice. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 99:1-99:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ITCS.2022.99

Abstract

We study the fundamental online k-server problem in a learning-augmented setting. While in the traditional online model, an algorithm has no information about the request sequence, we assume that there is given some advice (e.g. machine-learned predictions) on an algorithm’s decision. There is, however, no guarantee on the quality of the prediction and it might be far from being correct. Our main result is a learning-augmented variation of the well-known Double Coverage algorithm for k-server on the line (Chrobak et al., SIDMA 1991) in which we integrate predictions as well as our trust into their quality. We give an error-dependent competitive ratio, which is a function of a user-defined confidence parameter, and which interpolates smoothly between an optimal consistency, the performance in case that all predictions are correct, and the best-possible robustness regardless of the prediction quality. When given good predictions, we improve upon known lower bounds for online algorithms without advice. We further show that our algorithm achieves for any k an almost optimal consistency-robustness tradeoff, within a class of deterministic algorithms respecting local and memoryless properties. Our algorithm outperforms a previously proposed (more general) learning-augmented algorithm. It is remarkable that the previous algorithm crucially exploits memory, whereas our algorithm is memoryless. Finally, we demonstrate in experiments the practicability and the superior performance of our algorithm on real-world data.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Mathematics of computing → Mathematical optimization
Keywords
  • online k-server problem
  • competitive analysis
  • learning-augmented algorithms
  • untrusted predictions
  • consistency
  • robustness

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