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Search Games with Predictions (2401.01149v2)

Published 2 Jan 2024 in cs.GT and math.OC

Abstract: We introduce the study of search games between a mobile Searcher and an immobile Hider in a new setting in which the Searcher has some potentially erroneous information, i.e., a prediction on the Hider's position. The objective is to establish tight tradeoffs between the consistency of a search strategy (i.e., its worst case expected payoff assuming the prediction is correct) and its robustness (i.e., the worst case expected payoff with no assumptions on the quality of the prediction). Our study is the first to address the full power of mixed (randomized) strategies; previous work focused only on deterministic strategies, or relied on stochastic assumptions that do not guarantee worst-case robustness in adversarial situations. We give Pareto-optimal strategies for three fundamental problems, namely searching in discrete locations, searching with stochastic overlook, and searching in the infinite line. As part of our contribution, we provide a novel framework for proving optimal tradeoffs in search games which is applicable, more broadly, to any two-person zero-sum games in learning-augmented settings.

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References (52)
  1. Alpern, S. (2021). The faulty GPS problem: Shortest time paths in networks with unreliable directions. CoRR, abs/2111.09093.
  2. Search Theory: A Game Theoretic Perspective. Springer.
  3. The Theory of Search Games and Rendezvous. Kluwer Academic Publishers.
  4. Mining coal or finding terrorists: The expanding search paradigm. Operations Research, 61(2):265–279.
  5. Approximate solutions for expanding search games on general networks. Annals of Operations Research, 275(2):259–279.
  6. Searching a tree with signals: Routing mobile sensors for targets emitting radiation, chemicals or scents. CoRR, abs/2303.13378.
  7. Patrolling games. Operations research, 59(5):1246–1257.
  8. Alspach, B. (2004). Searching and sweeping graphs: a brief survey. Le matematiche, 59(1, 2):5–37.
  9. Angelopoulos, S. (2021). Online search with a hint. In Proceedings of the 12th Innovations in Theoretical Computer Science Conference (ITCS), pages 51:1–51:16.
  10. Angelopoulos, S. (2023). Competitive search in the line and the star with predictions. In 48th International Symposium on Mathematical Foundations of Computer Science, MFCS, volume 272 of LIPIcs, pages 12:1–12:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
  11. Online computation with untrusted advice. In 11th Innovations in Theoretical Computer Science Conference, ITCS 2020, pages 52:1–52:15.
  12. The expanding search ratio of a graph. Discrete Applied Mathematics, 260:51–65.
  13. Competitive search in a network. European Journal of Operational Research, 286(2):781–790.
  14. The flowtime network construction problem. IIE Transactions, 44(8):681–694.
  15. Searching in the plane. Information and Computation, 106:234–244.
  16. Graph searching with predictions. In ITCS, volume 251 of LIPIcs, pages 12:1–12:24. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
  17. Rendezvous search when marks are left at the starting points. Naval Research Logistics (NRL), 48(8):722–731.
  18. Yet more on the linear search problem. Israel Journal of Mathematics, 8:419–429.
  19. Searching a tree with permanently noisy advice. In ESA 2018-26th Annual European Symposium on Algorithms, pages 1–32.
  20. Convex optimization. Cambridge university press.
  21. Optimal robustness-consistency tradeoffs for learning-augmented metrical task systems. In International Conference on Artificial Intelligence and Statistics, pages 9377–9399. PMLR.
  22. Algorithms for distributional and adversarial pipelined filter ordering problems. ACM Transaction on Algorithms, 5(2):24:1–24:34.
  23. Online searching with turn cost. Theoretical Computer Science, 361:342–355.
  24. Online graph exploration with advice. In Structural Information and Communication Complexity: 19th International Colloquium, SIROCCO 2012, pages 267–278. Springer.
  25. Robustification of online graph exploration methods. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 36, pages 9732–9740.
  26. Gal, S. (1980). Search Games. Academic Press.
  27. Deterministic graph exploration with advice. ACM Transactions on Algorithms, 15(1):1–17.
  28. Improved approximation algorithms for the expanding search problem. In ESA, volume 274 of LIPIcs, pages 54:1–54:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
  29. Exact and approximation algorithms for the expanding search problem. INFORMS Journal on Computing, 34(1):281–296.
  30. Isaacs, R. (1965). Differential Games. Wiley, New York.
  31. Online searching. Operations Research, 49:234–244.
  32. A competitive analysis of algorithms for searching unknown scenes. Computational Geometry, 3(3):139–155.
  33. Optimal constructions of hybrid algorithms. Journal of Algorithms, 29(1):142–164.
  34. Searching in an unknown environment: an optimal randomized algorithm for the cow-path problem. Information and Computation, 131(1):63–80.
  35. Treasure hunt with advice. In Structural Information and Communication Complexity: 22nd International Colloquium, SIROCCO 2015, pages 328–341. Springer.
  36. Searching a fixed graph. In Proc. of the 23rd Int. Colloq. on Automata, Languages and Programming (ICALP), pages 280–289.
  37. Lower bounds for searching robots, some faulty. In Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, pages 447–453.
  38. Online peak-aware energy scheduling with untrusted advice. In e-Energy ’21: The Twelfth ACM International Conference on Future Energy Systems, pages 107–123. ACM.
  39. Pareto-optimal learning-augmented algorithms for online k-search problems. arXiv preprint arXiv:2211.06567.
  40. Robustness and consistency in linear quadratic control with untrusted predictions. Proc. ACM Meas. Anal. Comput. Syst., 6(1):18:1–18:35.
  41. Lidbetter, T. (2013). Search games with multiple hidden objects. SIAM Journal on Control and Optimization, 51(4):3056–3074.
  42. Repository of works on algorithms with predictions. https://algorithms-with-predictions.github.io/about. Accessed: 2022-09-01.
  43. The ultimate strategy to search on m𝑚mitalic_m rays? Theoretical Computer Science, 261(2):267–295.
  44. On-line parallel heuristics, processor scheduling and robot searching under the competitive framework. Theoretical Computer Science, 310(1–3):527–537.
  45. Competitive caching with machine learned advice. In Proceedings of the 35th International Conference on Machine Learning, ICML, pages 3302–3311.
  46. Algorithms with predictions. In Roughgarden, T., editor, Beyond the Worst-Case Analysis of Algorithms, page 646–662. Cambridge University Press.
  47. Advice complexity of treasure hunt in geometric terrains. Information and Computation, 281:104705.
  48. Improving online algorithms via ML predictions. In Advances in Neural Information Processing Systems, volume 31, pages 9661–9670.
  49. Ruckle, W. H. (1991). A discrete search game. In Stochastic Games And Related Topics: In Honor of Professor LS Shapley, pages 29–43. Springer.
  50. Pareto-optimal learning-augmented algorithms for online conversion problems. In Proceedings of the 34th Annual Conference on Neural Information Processing Systems (NeurIPS), volume 34.
  51. Optimal robustness-consistency trade-offs for learning-augmented online algorithms. In Proceedings of the 33rd Conference on Neural Information Processing Systems (NeurIPS).
  52. Weitzman, M. L. (1979). Optimal search for the best alternative. Econometrica, 4:641–654.
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