Autonomous Agents and Multi-Agent Systems

, Volume 29, Issue 1, pp 40–72 | Cite as

The complexity of multi-agent plan recognition

Article

Abstract

Multi-agent plan recognition (MAPR) seeks to identify the dynamic team structures and team plans from observations of the action sequences of a set of intelligent agents, based on a library of known team plans (plan library), and an evaluation function. It has important applications in decision support, team work, analyzing data from automated monitoring, surveillance, and intelligence analysis in general. We introduce a general model for MAPR that accommodates different representations of the plan library, and includes single agent plan recognition as a special case. Thus it provides an ideal substrate to investigate and contrast the complexities of single and multi-agent plan recognition. Using this model we generate theoretical insights on hardness, with practical implications. A key feature of these results is that they are baseline, i.e., the polynomial solvability results are given in terms of a compact and expressive plan language (context free language), while the hardness results are given in terms of a less compact language. Consequently the hardness results continue to hold in virtually all realistic plan languages, while the polynomial solvability results extend to the subsets of the context free plan language. In particular, we show that MAPR is in P (polynomial in the size of the plan library and the observation trace) if the number of agents is fixed (in particular 1) but NP-complete otherwise. If the number of agents is a variable, then even the one step MAPR problem is NP-complete. While these results pertain to abduction, we also investigate a related question: adaptation, i.e., the problem of refining the evaluation function based on feedback. We show that adaptation is also NP-hard for a variable number of agents, but easy for a single agent. These results establish a clear distinction between the hardnesses of single and multi-agent plan recognition even in idealized settings, indicating the necessity of a fundamentally different set of techniques for the latter.

Keywords

Plan recognition Multi-agent plan recognition Abductive reasoning Computational complexity 

References

  1. 1.
    Abdelbar, A. M. (2004). Approximating cost-based abduction is NP-hard. Artificial Intelligence, 159(1–2), 231–239.CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Avrahami-Zilberbrand, D., & Kaminka, G. A. (2007). Towards dynamic tracking of multi-agent teams: An initial report. In Proceedings of the AAAI Workshop on Plan, Activity and Intent Recognition (PAIR-07).Google Scholar
  3. 3.
    Avrahami-Zilberbrand, D., & Kaminka, G. A. (2007). Incorporating observer biases in keyhole plan recognition (efficiently!). In Proceedings of AAAI-07.Google Scholar
  4. 4.
    Banerjee, B., Kraemer, L., & Lyle, J. (2010). Multi-agent plan recognition: Formalization and algorithms. Proceedings of AAAI-10, Atlanta, GA (pp. 1059–1064).Google Scholar
  5. 5.
    Barry, D., & Hartigan, J. A. (1992). Product partition models for change point problems. The Annals of Statistics, 20, 260–279.CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Beetz, M., Gedikli, S., Kirchlechner, B., Maldonado, A. (2006). Camera-based observation of football games for analyzing multi-agent activities. In Proceedings of AAMAS.Google Scholar
  7. 7.
    Bernstein, D. S., Givan, R., Immerman, N., & Zilberstein, S. (2002). The complexity of decentralized control of Markov decision processes. Mathematics of Operations Research, 27, 819–840.CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Bishop, C. M. (2007). Pattern recognition and machine learning (information science and statistics). Heidelberg: Springer.Google Scholar
  9. 9.
    Boutilier, C., & Brafman, R. I. (2001). Partial-order planning with concurrent interacting actions. JAIR, 14(1), 105–136.MATHGoogle Scholar
  10. 10.
    Brenner, M. (2003). A multiagent planning language. In Proceedings of the ICAPS-03 workshop on PDDL (pp. 33–38).Google Scholar
  11. 11.
    Bui, H. (2003). A general model for online probabilistic plan recognition. In Proceedings of the International Joint Conference on Artificial Intelligence, IJCAI (pp. 1309–1315).Google Scholar
  12. 12.
    Castelfranchi, C., & Falcone, R. (1995). From single-agent to multi-agent: Challenges for plan recognition systems. In Proceedings of the IJCAI-95 Workshop on The Next Generation of Plan Recognition Systems (pp. 24–32).Google Scholar
  13. 13.
    Charniak, E., & Goldman, R. P. (1993). A Bayesian model of plan recognition. Artificial Intelligence, 64, 53–79.CrossRefGoogle Scholar
  14. 14.
    Cohen, P. R., Perrault, C. R., & Allen, J. F. (1981). Beyond question answering. In W. Lehnert & M. Ringle (Eds.), Strategies for natural language processing. Hillsdale, NJ: Lawrence Earlbaum Assoc.Google Scholar
  15. 15.
    Devaney, M., & Ram, A. (1998). Needles in a haystack: Plan recongition in large spatial domains involving multiple agents. In Proceedings of AAAI conference.Google Scholar
  16. 16.
    Erol, K., Hendler, J., & Nau, D. S. (1994). HTN planning: Complexity and expressivity. In Proceedings of the Twelfth National Conference on Artificial Intelligence (AAAI-94) (pp. 1123–1128). Seattle, WA: AAAI Press.Google Scholar
  17. 17.
    Garey, M. R., & Johnson, D. S. (1979). Computers and Intractability: A guide to the theory of NP-completeness. San Francisco, CA: W.H. Freeman and Co.MATHGoogle Scholar
  18. 18.
    Geib, C. (2004). Assessing the complexity of plan recognition. In Proceedings of AAAI-04.Google Scholar
  19. 19.
    Geib, C., & Goldman, R. (2003). Recognizing plan/goal abandonment. In Proceedings of IJCAI-03.Google Scholar
  20. 20.
    Geib, C. W., & Goldman, R. P. (2009). A probabilistic plan recognition algorithm based on plan tree grammars. Artificial Intelligence, 173(11), 1101–1132.CrossRefMathSciNetGoogle Scholar
  21. 21.
    Geib, C. W., & Goldman, R. P. (2002). Requirements for plan recognition in network security systems. In Proceedings of International Symposium on Recent Advances in Intrusion Detection.Google Scholar
  22. 22.
    Ghallab, M., Nau, D., & Traverso, P. (2004). Automated planning: Theory and practice. San Mateo, CA: Morgan Kaufmann Publishers.Google Scholar
  23. 23.
    Goldman, R. P., Geib, C. W., & Miller, C. A. (1999). A new model of plan recognition. In Proceedings of the Conference on Uncertainty in Artificial Intelligence.Google Scholar
  24. 24.
    Goldsmith, J., & Mundhenk, M. (2007). Competition adds complexity. In Proceedings of the NIPS.Google Scholar
  25. 25.
    Hongeng, S., & Nevatia, R. (2001). Multi-agent event recognition. In Proceedings of the Eighth IEEE International Conference on Computer Vision (Vol. 2, pp. 84–91).Google Scholar
  26. 26.
    Hsiao, J., Yuan, T., & Chang, R. S. (1992). An efficient algorithm for finding a maximum weight \(2\)-independent set on interval graphs. Information Processing Letters, 43(5), 229–235.CrossRefMATHMathSciNetGoogle Scholar
  27. 27.
    Huber, M. J., & Durfee, E. H. (1992). Plan recognition for real-world autonomous robots: Work in progress. In Working Notes of AAAI Symposium: Applications of AI to Real-World Autonomous Robots.Google Scholar
  28. 28.
    Ieong, S., & Shoham, Y. (2005). Marginal contribution nets: A compact representation scheme for coalitional games. In Proceedings of the 6th ACM Conference on Electronic Commerce (pp. 193–202).Google Scholar
  29. 29.
    Intille, S., & Bobick, A. (1999). A framework for recognizing multi-agent action from visual evidence. In Proceedings of AAAI.Google Scholar
  30. 30.
    Jensen, R. M., & Veloso, M. M. (2005). ASET: A multi-agent planning language with nondeterministic durative tasks for BDD-based fault tolerant planning. In Proceedings of the 2005 ICAPS Workshop on Multi-agent Planning and Scheduling (pp. 58–65).Google Scholar
  31. 31.
    Kaminka, G. A., & Bowling, M. (2002). Towards robust teams with many agents. In Proceeding of AAMAS-02.Google Scholar
  32. 32.
    Kaminka, G. A., Pynadath, D. V., & Tambe, M. (2002). Monitoring teams by overhearing: A multi-agent plan recognition approach. Journal of Artificial Intelligence Research, 17, 83–135.MATHGoogle Scholar
  33. 33.
    Kautz, H. A., & Allen, J. F. (1986). Generalized plan recognition. In Proceedings of AAAI.Google Scholar
  34. 34.
    Kebert, A., Banerjee, B., George, G., Solano, J., & Solano, W. (2013). Detecting distributed SQL injection attacks in a Eucalyptus cloud environment. In Proceedings of the 12th International Conference on Security and Management (SAM-13), Las Vegas, NV, July. Las Vegas, NV: CSREA Press.Google Scholar
  35. 35.
    Lesh, N., & Etzioni, O. (1995). Insights from machine learning for plan recognition. In Proceedings of the Workshop on The Next Generation of Plan Recognition Systems: Challenges for and Insight from Related Areas of AI (pp. 78–83).Google Scholar
  36. 36.
    Leyton-Brown, K., & Shoham, Y. (2008). Essentials of game theory: A concise multidisciplinary introduction. Synthesis Lectures on Artificial Intelligence and Machine Learning, 2(1), 1–88.CrossRefGoogle Scholar
  37. 37.
    Norman, M. D. T. J., Vasconcelos, W. W., & Sycara, K. (2011). Agent-oriented incremental team and activity recognition. In Proceedings of IJCAI.Google Scholar
  38. 38.
    Pynadath, D. V., & Wellman, M. P. (2000). Probabilistic state-dependent grammars for plan recognition. In Proceedings of the Conference on Uncertainty in Artificial Intelligence, UAI2000 (pp. 507–514). San Francisco, CA: Morgan Kaufmann Publishers.Google Scholar
  39. 39.
    Ramirez, M., & Geffner, H. (2009). Plan recognition as planning. In Proceedings of IJCAI.Google Scholar
  40. 40.
    Ramirez, M., & Geffner, H. (2010). Probabilistic plan recognition using off-the-shelf classical planners. Proceedings of AAAI-10, Atlanta, GA (pp. 1121–1126).Google Scholar
  41. 41.
    Ristad, E. S. (1993). The language complexity game. Cambridge, MA: MIT Press.Google Scholar
  42. 42.
    Sidner, C. (1985). Plan parsing for intended response recognition in discourse. Computational Intelligence, 1(1), 1–10.CrossRefGoogle Scholar
  43. 43.
    Sukthankar, G., & Sycara, K. (2006). Simultaneous team assignment and behavior recognition from spatio-temporal agent traces. In Proceedings of AAAI conference.Google Scholar
  44. 44.
    Sukthankar, G., & Sycara, K. (2008). Hypothesis pruning and ranking for large plan recognition problems. In Proceedings of AAAI.Google Scholar
  45. 45.
    Sukthankar, G., & Sycara, K. (2008). Robust and efficient plan recognition for dynamic multi-agent teams (short paper). In Proceedings of 7th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2008). International Foundation for Autonomous Agents and Multiagent Systems.Google Scholar
  46. 46.
    Sukthankar, G., & Sycara, K. (2011). Activity recognition for dynamic multi-agent teams. ACM Transactions on Intelligent Systems and Technology, 3(1), 18:1–18:24.Google Scholar
  47. 47.
    Tambe, M. (1995). Recursive agent and agent-group tracking in a real-time, dynamic environment. In Proceedings of International Conference on Multiagent Systems (pp. 368–375).Google Scholar
  48. 48.
    Tambe, M. (1996). Tracking dynamic team activity. In Proceedings of AAAI.Google Scholar
  49. 49.
    Vilain, M. (1990). Getting serious about parsing plans: A grammatical analysis of plan recognition. In Proceedings of AAAI-90.Google Scholar
  50. 50.
    Zhuo, H. H., & Li, L. (2011). Multi-agent plan recognition with partial team traces and plan libraries. In Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI-11) (pp. 484–489).Google Scholar
  51. 51.
    Zhuo, H. H., Yang, Q., & Kambhampati, S. (2012). Action-model based multi-agent plan recognition. In Proceedings of NIPS.Google Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Bikramjit Banerjee
    • 1
  • Jeremy Lyle
    • 1
  • Landon Kraemer
    • 1
  1. 1.University of Southern MississippiHattiesburgUSA

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