Prashant Doshi
ABSTRACT
State estimation consists of updating an agent's belief given executed actions and observed evidence to date. In single agent environments, the state estimation can be formalized using the Bayes filter. Exact estimation can be performed in simple cases, but approximate techniques, like particle filtering, have been used in more realistic cases. This paper extends the particle filter to multiagent settings resulting in the interactive particle filter. The main difficulty we tackle is that to fully represent an agent's beliefs in such environments, one has to specify probability distributions over the physical state and over the beliefs of other agents. This leads to interactive hierarchical belief systems first developed in game theory. Since the update of such beliefs proceeds recursively, the interactive particle filter samples and propagates on all levels of the belief hierarchy. We present algorithms, discuss some of their properties, and illustrate the performance of our implementation using simple examples.
- R. J. Aumann and A. Heifetz. Handbook of Game Theory with Economic Applications, volume 3. Elsevier Science, 2002.]]Google Scholar
- P. Battigalli and G. Bonanno. Recent results on belief, knowledge, and the epistemic foundations of game theory. Research in Economics, 53:149--225, 1999.]]Google ScholarCross Ref
- A. Brandenburger and E. Dekel. Hierarchies of beliefs and common knowledge. Journal of Economic Theory, 59:189--198, 1993.]]Google ScholarCross Ref
- A. Doucet, N. D. Freitas, and N. Gordon. Sequential Monte Carlo Methods in Practice. Springer Verlag, 2001.]]Google ScholarCross Ref
- R. Fagin, J. Halpern, Y. Moses, and M. Vardi. Reasoning about Knowledge. MIT Press, 1995.]] Google ScholarDigital Library
- D. Fox, W. Burgard, H. Kruppa, and S. Thrun. A probabilistic approach to collaborative multi-robot localization. Autonomous Robots on Heterogenous Multi-Robot Systems, 8(3), 2000.]] Google ScholarDigital Library
- P. Gmytrasiewicz and P. Doshi. Interactive pomdps: Properties and preliminary results. In AAMAS, pages 1374--1375, NYC, NY, 2004.]] Google ScholarDigital Library
- P. Gmytrasiewicz and P. Doshi. A framework for sequential planning in multiagent settings. Journal of AI Research, 23, 2005.]] Google ScholarDigital Library
- N. Gordon, D. Salmond, and A. Smith. Novel approach to non-linear/non-gaussian bayesian state estimation. IEEE Proceedings-F, 140(2):107--113, 1993.]]Google Scholar
- J. C. Harsanyi. Games with incomplete information played by 'bayesian' players. Mgmt. Science, 14(3):159--182, 1967.]] Google ScholarDigital Library
- A. Heifetz and D. Samet. Topology-free typology of beliefs. Journal of Economic Theory, 82:324--341, 1998.]]Google ScholarCross Ref
- L. Kaelbling, M. Littman, and A. Cassandra. Planning and acting in partially observable stochastic domains. Artificial Intelligence, 2, 1998.]]Google Scholar
- M. Li and P. Vitanyi. An Introduction to Kolmogorov Complexity and its Applications. Springer, 1997.]] Google ScholarDigital Library
- J. Mertens and S. Zamir. Formulation of bayesian analysis for games with incomplete information. International Journal of Game Theory, 14:1--29, 1985.]]Google ScholarDigital Library
- S. Russell and P. Norvig. Artificial Intelligence: A Modern Approach (Second Edition). Prentice Hall, 2003.]] Google ScholarDigital Library
- R. Smallwood and E. Sondik. The optimal control of partially observable markov decision processes over a finite horizon. Operations Research, 21:1071--1088, 1973.]]Google ScholarDigital Library
- S. Thrun. Monte carlo pomdps. In NIPS 12, pages 1064--1070, 2000.]]Google Scholar
Index Terms
- Approximating state estimation in multiagent settings using particle filters
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