Boosting Double Coverage for k-Server via Imperfect Predictions

We study the 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 (for example, machine-learned predictions) on an algorithm’s decision. There is, however...

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Veröffentlicht in:	Algorithmica Jg. 87; H. 11; S. 1477 - 1517
Hauptverfasser:	Lindermayr, Alexander, Megow, Nicole, Simon, Bertrand
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.11.2025 Springer Nature B.V Springer Verlag
Schlagworte:	Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Lower bounds Machine learning Mathematics of Computing Theory of Computation Learning-augmented algorithms Online k-server problem Competitive analysis Consistency Robustness Advice Imperfect predictions
ISSN:	0178-4617, 1432-0541
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Abstract	We study the 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 (for example, 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. in SIAM J Discret Math 4(2):172–181, 1991) in which we integrate predictions as well as our trust into their quality. We give an error-dependent worst-case performance guarantee, which is a function of a user-defined confidence parameter, and which interpolates smoothly between an optimal performance in case that all predictions are correct, and the best-possible performance 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 almost optimal guarantees, within a class of deterministic learning-augmented algorithms respecting local and memoryless properties. Our algorithm outperforms a previously proposed (more general) learning-augmented algorithm. It is noteworthy 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.
AbstractList	Abstract We study the 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 (for example, 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. in SIAM J Discret Math 4(2):172–181, 1991) in which we integrate predictions as well as our trust into their quality. We give an error-dependent worst-case performance guarantee, which is a function of a user-defined confidence parameter, and which interpolates smoothly between an optimal performance in case that all predictions are correct, and the best-possible performance 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 almost optimal guarantees, within a class of deterministic learning-augmented algorithms respecting local and memoryless properties. Our algorithm outperforms a previously proposed (more general) learning-augmented algorithm. It is noteworthy 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. We study the 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 (for example, 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. in SIAM J Discret Math 4(2):172–181, 1991) in which we integrate predictions as well as our trust into their quality. We give an error-dependent worst-case performance guarantee, which is a function of a user-defined confidence parameter, and which interpolates smoothly between an optimal performance in case that all predictions are correct, and the best-possible performance 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 almost optimal guarantees, within a class of deterministic learning-augmented algorithms respecting local and memoryless properties. Our algorithm outperforms a previously proposed (more general) learning-augmented algorithm. It is noteworthy 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. We study the 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 (for example, 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. in SIAM J Discret Math 4(2):172–181, 1991) in which we integrate predictions as well as our trust into their quality. We give an error-dependent worst-case performance guarantee, which is a function of a user-defined confidence parameter, and which interpolates smoothly between an optimal performance in case that all predictions are correct, and the best-possible performance 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 almost optimal guarantees, within a class of deterministic learning-augmented algorithms respecting local and memoryless properties. Our algorithm outperforms a previously proposed (more general) learning-augmented algorithm. It is noteworthy 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. We study the 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 (for example, 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. in SIAM J Discret Math 4(2):172–181, 1991) in which we integrate predictions as well as our trust into their quality. We give an error-dependent worst-case performance guarantee, which is a function of a user-defined confidence parameter, and which interpolates smoothly between an optimal performance in case that all predictions are correct, and the best-possible performance 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 almost optimal guarantees, within a class of deterministic learning-augmented algorithms respecting local and memoryless properties. Our algorithm outperforms a previously proposed (more general) learning-augmented algorithm. It is noteworthy 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.
Author	Simon, Bertrand Megow, Nicole Lindermayr, Alexander
Author_xml	– sequence: 1 givenname: Alexander surname: Lindermayr fullname: Lindermayr, Alexander email: linderal@uni-bremen.de organization: Faculty of Mathematics and Computer Science, University of Bremen – sequence: 2 givenname: Nicole surname: Megow fullname: Megow, Nicole organization: Faculty of Mathematics and Computer Science, University of Bremen – sequence: 3 givenname: Bertrand surname: Simon fullname: Simon, Bertrand organization: IN2P3 Computing Center, CNRS
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Snippet	We study the online k -server problem in a learning-augmented setting. While in the traditional online model, an algorithm has no information about the request... We study the online k -server problem in a learning-augmented setting. While in the traditional online model, an algorithm has no information about the request... We study the online k-server problem in a learning-augmented setting. While in the traditional online model, an algorithm has no information about the request... Abstract We study the online k -server problem in a learning-augmented setting. While in the traditional online model, an algorithm has no information about...
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SubjectTerms	Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Lower bounds Machine learning Mathematics of Computing Theory of Computation
Title	Boosting Double Coverage for k-Server via Imperfect Predictions
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