nips nips2003 nips2003-29 nips2003-29-reference knowledge-graph by maker-knowledge-mining

29 nips-2003-Applying Metric-Trees to Belief-Point POMDPs


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Author: Joelle Pineau, Geoffrey J. Gordon, Sebastian Thrun

Abstract: Recent developments in grid-based and point-based approximation algorithms for POMDPs have greatly improved the tractability of POMDP planning. These approaches operate on sets of belief points by individually learning a value function for each point. In reality, belief points exist in a highly-structured metric simplex, but current POMDP algorithms do not exploit this property. This paper presents a new metric-tree algorithm which can be used in the context of POMDP planning to sort belief points spatially, and then perform fast value function updates over groups of points. We present results showing that this approach can reduce computation in point-based POMDP algorithms for a wide range of problems. 1


reference text

[1] R. I. Brafman. A heuristic variable grid solution method for POMDPs. In Proceedings of the Fourteenth National Conference on Artificial Intelligence (AAAI), pages 727–733, 1997.

[2] A. Cassandra. http://www.cs.brown.edu/research/ai/pomdp/examples/index.html.

[3] J. H. Friendman, J. L. Bengley, and R. A. Finkel. An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3(3):209–226, 1977.

[4] M. Hauskrecht. Value-function approximations for partially observable Markov decision processes. Journal of Artificial Intelligence Research, 13:33–94, 2000.

[5] L. P. Kaelbling, M. L. Littman, and A. R. Cassandra. Planning and acting in partially observable stochastic domains. Artificial Intelligence, 101:99–134, 1998.

[6] A. W. Moore. Very fast EM-based mixture model clustering using multiresolution KD-trees. In Advances in Neural Information Processing Systems (NIPS), volume 11, 1999.

[7] A. W. Moore. The anchors hierarchy: Using the triangle inequality to survive high dimensional data. Technical Report CMU-RI-TR-00-05, Carnegie Mellon, 2000.

[8] J. Pineau, G. Gordon, and S. Thrun. Point-based value iteration: An anytime algorithm for POMDPs. In International Joint Conference on Artificial Intelligence (IJCAI), 2003.

[9] K.-M. Poon. A fast heuristic algorithm for decision-theoretic planning. Master’s thesis, The Hong-Kong University of Science and Technology, 2001.

[10] P. Poupart and C. Boutilier. Value-directed compression of POMDPs. In Advances in Neural Information Processing Systems (NIPS), volume 15, 2003.

[11] N. Roy and G. Gordon. Exponential family PCA for belief compression in POMDPs. In Advances in Neural Information Processing Systems (NIPS), volume 15, 2003.

[12] J. K. Uhlmann. Satisfying general proximity/similarity queries with metric trees. Information Processing Letters, 40:175–179, 1991.

[13] R. Zhou and E. A. Hansen. An improved grid-based approximation algorithm for POMDPs. In Proceedings of the 17th International Joint Conference on Artificial Intelligence (IJCAI), 2001. 3 The coffee domain is known to have an intrinsic dimensionality of 7 [10]. We do not know the intrinsic dimensionality of the Tag domain, but many robot applications produce belief points that exist in sub-dimensional manifolds [11].