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Rényi-Ulam Games and Online Computation with Imperfect Advice

Authors Spyros Angelopoulos , Shahin Kamali

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Spyros Angelopoulos
  • CNRS and LIP6-Sorbonne University, Paris, France
Shahin Kamali
  • York University, Toronto, Canada

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Spyros Angelopoulos and Shahin Kamali. Rényi-Ulam Games and Online Computation with Imperfect Advice. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 13:1-13:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


We study the nascent setting of online computation with imperfect advice, in which the online algorithm is enhanced by some prediction encoded in the form of an imperfect, and possibly erroneous binary string. The algorithm is oblivious to the advice error, but defines a desired tolerance, namely an upper bound on the number of erroneous advice bits it can tolerate. This is a model that generalizes the Pareto-based advice model, in which the performance of the algorithm is only evaluated at the extreme values of error (namely, if the advice has either no errors, or if it is generated adversarially). It also subsumes the model in which the algorithm elicits a prediction on the online sequence, via imperfect responses to a number of binary queries. In this work, we establish connections between games with a lying responder, also known as Rényi-Ulam games, and the design and analysis of online algorithms with imperfect advice. Specifically, we demonstrate how to obtain upper and lower bounds on the competitive ratio for important online problems such as time-series search, online bidding, and fractional knapsack. Our techniques provide the first lower bounds for online problems in this model. We also highlight and exploit connections between competitive analysis with imperfect advice and fault-tolerance in multiprocessor systems. Last, we show how to waive the dependence on the tolerance parameter, by means of resource augmentation and robustification.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Online computation
  • Rényi-Ulam games
  • query models
  • beyond worst-case analysis


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  1. Iftikhar Ahmad, Marcus Pirron, and Günter Schmidt. Analysis of threat based algorithm using different performance measures. RAIRO: Operations Research, 55:2393, 2021. Google Scholar
  2. Susanne Albers, Arindam Khan, and Leon Ladewig. Improved online algorithms for knapsack and gap in the random order model. Algorithmica, 83(6):1750-1785, 2021. Google Scholar
  3. Keerti Anand, Rong Ge, Amit Kumar, and Debmalya Panigrahi. A regression approach to learning-augmented online algorithms. Advances in Neural Information Processing Systems, 34:30504-30517, 2021. Google Scholar
  4. Spyros Angelopoulos. Online search with a hint. In Proceedings of the 12th Innovations in Theoretical Computer Science Conference (ITCS), pages 51:1-51:16, 2021. Google Scholar
  5. Spyros Angelopoulos, Christoph Dürr, Shendan Jin, Shahin Kamali, and Marc P. Renault. Online computation with untrusted advice. In Proceedings of the 11th International Conference on Innovations in Theoretical Computer Science (ITCS), pages 52:1-52:15, 2020. Google Scholar
  6. Spyros Angelopoulos and Shahin Kamali. Contract scheduling with predictions. Journal of Artificial Intelligence Research, 77:395-426, 2023. Google Scholar
  7. Spyros Angelopoulos, Shahin Kamali, and Dehou Zhang. Online search with best-price and query-based predictions. In Proceedings of the 36th AAAI Conference on Artificial Intelligence, pages 9652-9660, 2022. Google Scholar
  8. Hans-Joachim Böckenhauer, Dennis Komm, Rastislav Královic, and Richard Královic. On the advice complexity of the k-server problem. J. Comput. Syst. Sci., 86:159-170, 2017. Google Scholar
  9. Hans-Joachim Böckenhauer, Dennis Komm, Rastislav Královic, Richard Královic, and Tobias Mömke. Online algorithms with advice: The tape model. Inf. Comput., 254:59-83, 2017. Google Scholar
  10. Joan Boyar, Lene M. Favrholdt, Christian Kudahl, Kim S. Larsen, and Jesper W. Mikkelsen. Online algorithms with advice: A survey. ACM Comput. Surv., 50(2):19:1-19:34, 2017. Google Scholar
  11. Joan Boyar, Kim S. Larsen, and Abyayananda Maiti. A comparison of performance measures via online search. Theoretical Computer Science, 532:2-13, 2014. Google Scholar
  12. Niv Buchbinder and Joseph Naor. Improved bounds for online routing and packing via a primal-dual approach. In Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 293-304. IEEE, 2006. Google Scholar
  13. Niv Buchbinder and Joseph Naor. Online primal-dual algorithms for covering and packing. Math. Oper. Res., 34(2):270-286, 2009. Google Scholar
  14. Ying Cao, Bo Sun, and Danny Tsang. Optimal online algorithms for one-way trading and online knapsack problems: A unified competitive analysis. In Proceedings of the 59th IEEE Conference on Decision and Control (CDC), pages 1064-1069, 2020. Google Scholar
  15. Marek Chrobak and Claire Kenyon-Mathieu. SIGACT news online algorithms column 10: Competitiveness via doubling. SIGACT News, 37(4):115-126, 2006. Google Scholar
  16. Jhoirene Clemente, Juraj Hromkovič, Dennis Komm, and Christian Kudahl. Advice complexity of the online search problem. In Proceedings of the 27th International Workshop on Combinatorial Algorithms (IWOCA), pages 203-212, 2016. Google Scholar
  17. Peter Damaschke, Phuong Hoai Ha, and Philippas Tsigas. Online search with time-varying price bounds. Algorithmica, 55(4):619-642, 2009. Google Scholar
  18. Stefan Dobrev, Rastislav Královič, and Dana Pardubská. Measuring the problem-relevant information in input. RAIRO Theor. Informatics Appl., 43(3):585-613, 2009. Google Scholar
  19. Ran El-Yaniv, Amos Fiat, Richard M Karp, and Gordon Turpin. Optimal search and one-way trading online algorithms. Algorithmica, 30(1):101-139, 2001. Google Scholar
  20. Yuval Emek, Pierre Fraigniaud, Amos Korman, and Adi Rosén. Online computation with advice. Theoretical Computer Science, 412(24):2642-2656, 2011. Google Scholar
  21. Shmuel Gal. A general search game. Israel Journal of Mathematics, 12:32-45, 1972. Google Scholar
  22. Sungjin Im, Ravi Kumar, Aditya Petety, and Manish Purohit. Parsimonious learning-augmented caching. In Proceedsings of the 39th International Conference on Machine Learning (ICML), pages 9588-9601. PMLR, 2022. Google Scholar
  23. Sungjin Im, Ravi Kumar, Mahshid Montazer Qaem, and Manish Purohit. Online knapsack with frequency predictions. In Proceedings of the 34th Annual Conference on Neural Information Processing Systems (NeurIPS), pages 2733-2743, 2021. Google Scholar
  24. Thomas Kesselheim, Klaus Radke, Andreas Tönnis, and Berthold Vöcking. Primal beats dual on online packing LPs in the random-order model. SIAM J. Comput., 47(5):1939-1964, 2018. Google Scholar
  25. Dennis Komm. An Introduction to Online Computation - Determinism, Randomization, Advice. Texts in Theoretical Computer Science. An EATCS Series. Springer, 2016. Google Scholar
  26. Russell Lee, Jessica Maghakian, Mohammad H. Hajiesmaili, Jian Li, Ramesh K. Sitaraman, and Zhenhua Liu. Online peak-aware energy scheduling with untrusted advice. In Proceedings of the 12th ACM International Conference on Future Energy Systems (eEnergy), pages 107-123. ACM, 2021. Google Scholar
  27. Bin Li and Steven CH Hoi. Online portfolio selection: A survey. ACM Computing Surveys (CSUR), 46(3):1-36, 2014. Google Scholar
  28. Tongxin Li, Ruixiao Yang, Guannan Qu, Guanya Shi, Chenkai Yu, Adam Wierman, and Steven H. Low. Robustness and consistency in linear quadratic control with untrusted predictions. Proc. ACM Meas. Anal. Comput. Syst., 6(1):18:1-18:35, 2022. Google Scholar
  29. Alexander Lindermayr and Nicole Megow. Repository of works on algorithms with predictions., 2023. Accessed: 2023-04-01.
  30. Julian Lorenz, Konstantinos Panagiotou, and Angelika Steger. Optimal algorithms for k-search with application in option pricing. Algorithmica, 55(2):311-328, 2009. Google Scholar
  31. Thodoris Lykouris and Sergei Vassilvitskii. Competitive caching with machine learned advice. J. ACM, 68(4):24:1-24:25, 2021. Google Scholar
  32. Florence Jessie MacWilliams and Neil James Alexander Sloane. The theory of error correcting codes, volume 16. Elsevier, 1977. Google Scholar
  33. Arya Mazumdar and Barna Saha. Clustering with noisy queries. In Proceedings of the 31st Conference on Neural Information Processing Systems (NeurIPS), pages 5788-5799. NIPS, 2017. Google Scholar
  34. Michael Mitzenmacher and Sergei Vassilvitskii. Algorithms with predictions. In Beyond the Worst-Case Analysis of Algorithms, pages 646-662. Cambridge University Press, 2020. Google Scholar
  35. Manish Purohit, Zoya Svitkina, and Ravi Kumar. Improving online algorithms via ML predictions. In Proceedings of the 32nd Conference on Neural Information Processing Systems (NeurIPS), pages 9661-9670, 2018. Google Scholar
  36. Ronald L. Rivest, Albert R. Meyer, Daniel J. Kleitman, Karl Winklmann, and Joel Spencer. Coping with errors in binary search procedures. J. Comput. Syst. Sci., 20(3):396-404, 1980. Google Scholar
  37. Daniel Sleator and Robert E. Tarjan. Amortized efficiency of list update and paging rules. Communications of the ACM, 28:202-208, 1985. Google Scholar
  38. Bo Sun, Ali Zeynali, Tongxin Li, Mohammad Hajiesmaili, Adam Wierman, and Danny HK Tsang. Competitive algorithms for the online multiple knapsack problem with application to electric vehicle charging. Proceedings of the ACM on Measurement and Analysis of Computing Systems, 4(3):1-32, 2020. Google Scholar
  39. Alexander Wei and Fred Zhang. Optimal robustness-consistency trade-offs for learning-augmented online algorithms. In Proceedings of the 33rd Conference on Neural Information Processing Systems (NeurIPS), 2020. Google Scholar
  40. Yinfeng Xu, Wenming Zhang, and Feifeng Zheng. Optimal algorithms for the online time series search problem. Theoretical Computer Science, 412(3):192-197, 2011. Google Scholar
  41. Yunhong Zhou, Deeparnab Chakrabarty, and Rajan Lukose. Budget constrained bidding in keyword auctions and online knapsack problems. In Proceedings of the International Workshop on Internet and Network Economics (WINE), pages 566-576. Springer, 2008. Google Scholar
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