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Online State Exploration: Competitive Worst Case and Learning-Augmented Algorithms

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Machine Learning and Knowledge Discovery in Databases: Research Track (ECML PKDD 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14172))

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Abstract

This paper introduces the online state exploration problem. In the problem, there is a hidden d-dimensional target state. We are given a distance function between different states in the space and a penalty function depending on the current state for each incorrect guess. The goal is to move to a vector that dominates the target state starting from the origin in the d-dimensional space while minimizing the total distance and penalty cost. This problem generalizes several natural online discrete optimization problems such as multi-dimensional knapsack cover, cow path, online bidding, and online search. For online state exploration, the paper gives results in the worst-case competitive analysis model and in the online algorithms augmented with the prediction model. The results extend and generalize many known results in the online setting.

All authors (ordered alphabetically) have equal contributions.

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Notes

  1. 1.

    The lower bound 4 of worst case algorithms is the best possible robustness ratio.

  2. 2.

    The code is available at https://github.com/Chenyang-1995/Online-State-Exploration.

References

  1. Ai, L., Wu, X., Huang, L., Huang, L., Tang, P., Li, J.: The multi-shop ski rental problem. In: SIGMETRICS. pp. 463–475. ACM (2014)

    Google Scholar 

  2. Anand, K., Ge, R., Kumar, A., Panigrahi, D.: A regression approach to learning-augmented online algorithms. In: NeurIPS, vol. 34 (2021)

    Google Scholar 

  3. Anand, K., Ge, R., Panigrahi, D.: Customizing ML predictions for online algorithms. In: ICML. Proceedings of Machine Learning Research, vol. 119, pp. 303–313. PMLR (2020)

    Google Scholar 

  4. Angelopoulos, S.: Online search with a hint. In: ITCS. LIPIcs, vol. 185, pp. 51:1–51:16 (2021)

    Google Scholar 

  5. Antoniadis, A., Gouleakis, T., Kleer, P., Kolev, P.: Secretary and online matching problems with machine learned advice. In: NeurIPS (2020)

    Google Scholar 

  6. Azar, Y.: On-line load balancing. In: Fiat, A., Woeginger, G.J. (eds.) Online Algorithms. LNCS, vol. 1442, pp. 178–195. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0029569

    Chapter  Google Scholar 

  7. Baeza-Yates, R.A., Culberson, J.C., Rawlins, G.J.E.: Searching in the plane. Inf. Comput. 106(2), 234–252 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bamas, É., Maggiori, A., Svensson, O.: The primal-dual method for learning augmented algorithms. In: NeurIPS (2020)

    Google Scholar 

  9. Charikar, M., Chekuri, C., Feder, T., Motwani, R.: Incremental clustering and dynamic information retrieval. SIAM J. Comput. 33(6), 1417–1440 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chrobak, M., Kenyon, C., Noga, J., Young, N.E.: Incremental medians via online bidding. Algorithmica 50(4), 455–478 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Demaine, E.D., Fekete, S.P., Gal, S.: Online searching with turn cost. Theor. Comput. Sci. 361(2–3), 342–355 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  12. Dütting, P., Lattanzi, S., Leme, R.P., Vassilvitskii, S.: Secretaries with advice. In: EC, pp. 409–429. ACM (2021)

    Google Scholar 

  13. Epstein, L., Levin, A.: Randomized algorithms for online bounded bidding. Inf. Process. Lett. 110(12–13), 503–506 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Im, S., Kumar, R., Qaem, M.M., Purohit, M.: Non-clairvoyant scheduling with predictions. In: SPAA, pp. 285–294. ACM (2021)

    Google Scholar 

  15. Jiang, Z., Panigrahi, D., Sun, K.: Online algorithms for weighted paging with predictions. In: ICALP, pp. 69:1–69:18 (2020)

    Google Scholar 

  16. Kao, M., Ma, Y., Sipser, M., Yin, Y.L.: Optimal constructions of hybrid algorithms. J. Algorithms 29(1), 142–164 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  17. Kao, M., Reif, J.H., Tate, S.R.: Searching in an unknown environment: an optimal randomized algorithm for the cow-path problem. Inf. Comput. 131(1), 63–79 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  18. Lattanzi, S., Lavastida, T., Moseley, B., Vassilvitskii, S.: Online scheduling via learned weights. In: SODA, pp. 1859–1877 (2020)

    Google Scholar 

  19. Lotker, Z., Patt-Shamir, B., Rawitz, D.: Rent, lease, or buy: randomized algorithms for multislope ski rental. SIAM J. Discret. Math. 26(2), 718–736 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  20. Lykouris, T., Vassilvitskii, S.: Competitive caching with machine learned advice. In: ICML, Proceedings of Machine Learning Research, vol. 80, pp. 3302–3311. PMLR (2018)

    Google Scholar 

  21. Meyerson, A.: The parking permit problem. In: FOCS, pp. 274–284. IEEE Computer Society (2005)

    Google Scholar 

  22. Mitzenmacher, M., Vassilvitskii, S.: Algorithms with predictions. In: Beyond the Worst-Case Analysis of Algorithms, pp. 646–662. Cambridge University Press (2020)

    Google Scholar 

  23. Purohit, M., Svitkina, Z., Kumar, R.: Improving online algorithms via ML predictions. In: NeurIPS, pp. 9684–9693 (2018)

    Google Scholar 

  24. Rohatgi, D.: Near-optimal bounds for online caching with machine learned advice. In: SODA, pp. 1834–1845 (2020)

    Google Scholar 

  25. Wang, S., Li, J., Wang, S.: Online algorithms for multi-shop ski rental with machine learned advice. In: NeurIPS (2020)

    Google Scholar 

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Acknowledgements

Chenyang Xu was supported in part by Science and Technology Innovation 2030 -“The Next Generation of Artificial Intelligence” Major Project No.2018AAA0100900, and the Dean’s Fund of Shanghai Key Laboratory of Trustworthy Computing, East China Normal University. Sungjin Im was supported in part by NSF grants CCF-1844939 and CCF-2121745. Benjamin Moseley was supported in part by a Google Research Award, an Infor Research Award, a Carnegie Bosch Junior Faculty Chair, and NSF grants CCF-2121744 and CCF-1845146. Ruilong Zhang was supported by NSF grant CCF-1844890.

Author information

Authors and Affiliations

  1. Electrical Engineering and Computer Science, University of California at Merced, Merced, CA, USA

    Sungjin Im

  2. Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, USA

    Benjamin Moseley

  3. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China

    Chenyang Xu

  4. Department of Computer Science and Engineering, University at Buffalo, Buffalo, NY, USA

    Ruilong Zhang

Authors
  1. Sungjin Im
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  2. Benjamin Moseley
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  3. Chenyang Xu
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  4. Ruilong Zhang
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Corresponding authors

Correspondence to Sungjin Im , Benjamin Moseley , Chenyang Xu or Ruilong Zhang .

Editor information

Editors and Affiliations

  1. University of Michigan, Ann Arbor, MI, USA

    Danai Koutra

  2. University of Vienna, Vienna, Austria

    Claudia Plant

  3. Max Planck Institute for Software Systems, Kaiserslautern, Germany

    Manuel Gomez Rodriguez

  4. Politecnico di Torino, Turin, Italy

    Elena Baralis

  5. CENTAI, Turin, Italy

    Francesco Bonchi

Ethics declarations

The current paper is a theoretical work that explores various ideas and concepts related to the topic which aims to strengthen the traditional worst-case algorithm via machine learning advice. As such, there are no ethical issues associated with the research presented here. The paper includes some experiments which aims to verify the efficiency of the proposed algorithms. But this paper does not involve any experiments or studies that involve human and no personal information or data is used in the analysis. Instead, the focus is on developing theoretical models and frameworks that can help to advance our understanding of the subject matter.

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Im, S., Moseley, B., Xu, C., Zhang, R. (2023). Online State Exploration: Competitive Worst Case and Learning-Augmented Algorithms. In: Koutra, D., Plant, C., Gomez Rodriguez, M., Baralis, E., Bonchi, F. (eds) Machine Learning and Knowledge Discovery in Databases: Research Track. ECML PKDD 2023. Lecture Notes in Computer Science(), vol 14172. Springer, Cham. https://doi.org/10.1007/978-3-031-43421-1_20

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  • DOI: https://doi.org/10.1007/978-3-031-43421-1_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-43420-4

  • Online ISBN: 978-3-031-43421-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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