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Double Coverage with Machine-Learned Advice

Authors Alexander Lindermayr , Nicole Megow , Bertrand Simon

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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

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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)


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
  • online k-server problem
  • competitive analysis
  • learning-augmented algorithms
  • untrusted predictions
  • consistency
  • robustness


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  1. Spyros Angelopoulos, Christoph Dürr, Shendan Jin, Shahin Kamali, and Marc P. Renault. Online computation with untrusted advice. In ITCS, volume 151 of LIPIcs, pages 52:1-52:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. Google Scholar
  2. Antonios Antoniadis, Christian Coester, Marek Eliás, Adam Polak, and Bertrand Simon. Online metric algorithms with untrusted predictions. In ICML, volume 119 of Proceedings of Machine Learning Research, pages 345-355. PMLR, 2020. Google Scholar
  3. Antonios Antoniadis, Carsten Fischer, and Andreas Tönnis. A collection of lower bounds for online matching on the line. In LATIN, volume 10807 of Lecture Notes in Computer Science, pages 52-65. Springer, 2018. Google Scholar
  4. Antonios Antoniadis, Themis Gouleakis, Pieter Kleer, and Pavel Kolev. Secretary and online matching problems with machine learned advice. In NeurIPS, 2020. Google Scholar
  5. Yossi Azar, Stefano Leonardi, and Noam Touitou. Flow time scheduling with uncertain processing time. In STOC, pages 1070-1080. ACM, 2021. Google Scholar
  6. Étienne Bamas, Andreas Maggiori, Lars Rohwedder, and Ola Svensson. Learning augmented energy minimization via speed scaling. In NeurIPS, 2020. Google Scholar
  7. Étienne Bamas, Andreas Maggiori, and Ola Svensson. The primal-dual method for learning augmented algorithms. In NeurIPS, 2020. Google Scholar
  8. Soumya Banerjee. Improving online rent-or-buy algorithms with sequential decision making and ML predictions. In NeurIPS, 2020. Google Scholar
  9. Yair Bartal, Béla Bollobás, and Manor Mendel. Ramsey-type theorems for metric spaces with applications to online problems. J. Comput. Syst. Sci., 72(5):890-921, 2006. Google Scholar
  10. Yair Bartal and Elias Koutsoupias. On the competitive ratio of the work function algorithm for the k-server problem. Theor. Comput. Sci., 324(2-3):337-345, 2004. Google Scholar
  11. Allan Borodin and Ran El-Yaniv. Online computation and competitive analysis. Cambridge University Press, 1998. Google Scholar
  12. Sébastien Bubeck, Michael B. Cohen, Yin Tat Lee, James R. Lee, and Aleksander Madry. k-server via multiscale entropic regularization. In STOC, pages 3-16. ACM, 2018. Google Scholar
  13. Niv Buchbinder, Christian Coester, and Joseph (Seffi) Naor. Online k-taxi via double coverage and time-reverse primal-dual. In IPCO, volume 12707 of Lecture Notes in Computer Science, pages 15-29. Springer, 2021. Google Scholar
  14. Ashish Chiplunkar and Sundar Vishwanathan. Randomized memoryless algorithms for the weighted and the generalized k-server problems. ACM Trans. Algorithms, 16(1):14:1-14:28, 2020. Google Scholar
  15. Eunjoon Cho, Seth A. Myers, and Jure Leskovec. Friendship and mobility: user movement in location-based social networks. In KDD, pages 1082-1090. ACM, 2011. Google Scholar
  16. Marek Chrobak, Howard J. Karloff, T. H. Payne, and Sundar Vishwanathan. New results on server problems. SIAM J. Discret. Math., 4(2):172-181, 1991. Google Scholar
  17. Marek Chrobak and Lawrence L. Larmore. An optimal on-line algorithm for k-servers on trees. SIAM J. Comput., 20(1):144-148, 1991. Google Scholar
  18. Paul Dütting, Silvio Lattanzi, Renato Paes Leme, and Sergei Vassilvitskii. Secretaries with advice. In EC, pages 409-429. ACM, 2021. Google Scholar
  19. Sreenivas Gollapudi and Debmalya Panigrahi. Online algorithms for rent-or-buy with expert advice. In ICML, volume 97 of Proceedings of Machine Learning Research, pages 2319-2327. PMLR, 2019. Google Scholar
  20. Sungjin Im, Ravi Kumar, Mahshid Montazer Qaem, and Manish Purohit. Non-clairvoyant scheduling with predictions. In SPAA, pages 285-294. ACM, 2021. Google Scholar
  21. Manoel Leandro L Junior, AD Doria Neto, and Jorge D Melo. The k-server problem: a reinforcement learning approach. In IJCNN, 2005. Google Scholar
  22. Elias Koutsoupias. The k-server problem. Comput. Sci. Rev., 3(2):105-118, 2009. Google Scholar
  23. Elias Koutsoupias and Christos H. Papadimitriou. On the k-server conjecture. J. ACM, 42(5):971-983, 1995. Google Scholar
  24. Elias Koutsoupias and David Scot Taylor. The CNN problem and other k-server variants. Theor. Comput. Sci., 324(2-3):347-359, 2004. Google Scholar
  25. Tim Kraska, Alex Beutel, Ed H. Chi, Jeffrey Dean, and Neoklis Polyzotis. The case for learned index structures. In SIGMOD Conference, pages 489-504. ACM, 2018. Google Scholar
  26. Ravi Kumar, Manish Purohit, Aaron Schild, Zoya Svitkina, and Erik Vee. Semi-online bipartite matching. In ITCS, volume 124 of LIPIcs, pages 50:1-50:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. Google Scholar
  27. Silvio Lattanzi, Thomas Lavastida, Benjamin Moseley, and Sergei Vassilvitskii. Online scheduling via learned weights. In SODA, pages 1859-1877. SIAM, 2020. Google Scholar
  28. Thomas Lavastida, Benjamin Moseley, R. Ravi, and Chenyang Xu. Learnable and instance-robust predictions for online matching, flows and load balancing. In ESA, volume 204 of LIPIcs, pages 59:1-59:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. Google Scholar
  29. M. Leandro Costa, C. A. Araujo Padilha, J. Dantas Melo, and A. Duarte Doria Neto. Hierarchical reinforcement learning and parallel computing applied to the k-server problem. IEEE Latin America Transactions, 14(10):4351-4357, 2016. Google Scholar
  30. Alexander Lindermayr. Learning-augmented online algorithms for the 2-server problem on the line and generalizations. Master’s thesis, University of Bremen, Germany, 2020. Google Scholar
  31. Ramon Augusto Sousa Lins, Adrião Duarte Dória Neto, and Jorge Dantas de Melo. Deep reinforcement learning applied to the k-server problem. Expert Syst. Appl., 135:212-218, 2019. Google Scholar
  32. Pinyan Lu, Xuandi Ren, Enze Sun, and Yubo Zhang. Generalized sorting with predictions. In Symposium on Simplicity in Algorithms (SOSA), pages 111-117. SIAM, 2021. Google Scholar
  33. Thodoris Lykouris and Sergei Vassilvitskii. Competitive caching with machine learned advice. In ICML, volume 80 of Proceedings of Machine Learning Research, pages 3302-3311. PMLR, 2018. Google Scholar
  34. Mohammad Mahdian, Hamid Nazerzadeh, and Amin Saberi. Allocating online advertisement space with unreliable estimates. In EC, pages 288-294. ACM, 2007. Google Scholar
  35. Mark S. Manasse, Lyle A. McGeoch, and Daniel Dominic Sleator. Competitive algorithms for on-line problems. In STOC, pages 322-333. ACM, 1988. Google Scholar
  36. Mark S. Manasse, Lyle A. McGeoch, and Daniel Dominic Sleator. Competitive algorithms for server problems. J. Algorithms, 11(2):208-230, 1990. Google Scholar
  37. Andres Muñoz Medina and Sergei Vassilvitskii. Revenue optimization with approximate bid predictions. In NIPS, pages 1858-1866, 2017. Google Scholar
  38. Michael Mitzenmacher. A model for learned bloom filters and optimizing by sandwiching. In NeurIPS, pages 462-471, 2018. Google Scholar
  39. Michael Mitzenmacher. Scheduling with predictions and the price of misprediction. In ITCS, volume 151 of LIPIcs, pages 14:1-14:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. Google Scholar
  40. Manish Purohit, Zoya Svitkina, and Ravi Kumar. Improving online algorithms via ML predictions. In NeurIPS, pages 9684-9693, 2018. Google Scholar
  41. Dhruv Rohatgi. Near-optimal bounds for online caching with machine learned advice. In SODA, pages 1834-1845. SIAM, 2020. Google Scholar
  42. Shai Shalev-Shwartz and Shai Ben-David. Understanding Machine Learning - From Theory to Algorithms. Cambridge University Press, 2014. Google Scholar
  43. Daniel Dominic Sleator and Robert Endre Tarjan. Amortized efficiency of list update and paging rules. Commun. ACM, 28(2):202-208, 1985. Google Scholar
  44. Shufan Wang, Jian Li, and Shiqiang Wang. Online algorithms for multi-shop ski rental with machine learned advice. In NeurIPS, 2020. Google Scholar
  45. Alexander Wei. Better and simpler learning-augmented online caching. In APPROX, volume 176 of LIPIcs, pages 60:1-60:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. Google Scholar
  46. Alexander Wei and Fred Zhang. Optimal robustness-consistency trade-offs for learning-augmented online algorithms. In NeurIPS, 2020. Google Scholar
  47. Wenming Zhang and Yongxi Cheng. A new upper bound on the work function algorithm for the k-server problem. J. Comb. Optim., 39(2):509-518, 2020. Google Scholar
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