Abstract
Search in abstract spaces has been shown to produce useful admissible heuristic estimates in deterministic domains. We show in this paper how to generalize these results to search in stochastic domains. Solving stochastic optimization problems is significantly harder than solving their deterministic counterparts. Designing admissible heuristics for stochastic domains is also much harder. Therefore, deriving such heuristics automatically using abstraction is particularly beneficial. We analyze this approach both theoretically and empirically and show that it produces significant computational savings when used in conjunction with the heuristic search algorithm LAO*.
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References
Barto, A.G., Mahadevan, S.: Recent Advances in Hierarchical Reinforcement Learning. Discrete Event Dynamic Systems: Theory and Applications 13, 41–77 (2003)
Boutilier, C., Dearden, R.: Approximating Value Trees in Structured Dynamic Programming. In: Proc. of the Thirteenth International Conference on Machine Learning (1996)
Culberson, J.C., Schaeffer, J.: Pattern Databases. Computational Intelligence 14(3), 318–334 (1998)
Dean, T., Pack Kaelbling, L., Kirman, J., Nicholson, A.: Planning with Deadlines in Stochastic Domains. In: Proc. of the Eleventh National Conference on Artificial Intelligence, pp. 574–579 (1993)
Dearden, R., Boutilier, C.: Abstraction and Approximate Decision-Theoretic Planning. Artificial Intelligence 89, 219–283 (1997)
Hansen, E.A., Zilberstein, S.: LAO*: A Heuristic Search Algorithm that Finds Solutions with Loops. Artificial Intelligence 129(1-2), 35–62 (2001)
Holte, R.C., Drummond, C., Perez, M.B., Zimmer, R.M., MacDonald, A.J.: Searching with Abstractions: A Unifying Framework and New High-Performance Algorithm. In: Proc. of the Canadian Artificial Intelligence Conference, pp. 263–270 (1994)
Holte, R.C., Perez, M.B., Zimmer, R.M., MacDonald, A.J.: Hierarchical A*: Searching Abstraction Hierarchies Efficiently. In: Proc. of the Thirteenth National Conference on Artificial Intelligence, pp. 530–535 (1996)
Korf, R.E., Felner, A.: Disjoint Pattern Database Heuristics. Artificial Intelligence 134(1-2), 9–22 (2002)
Korf, R.E.: Finding Optimal Solutions to Rubik’s Cube Using Pattern Databases. In: Proc. of the Fourteenth National Conference on Artificial Intelligence, pp. 700–705 (1997)
Pearl, J.: Heuristics. Addison-Wesley, Reading (1984)
Preditis, A.: Machine Discovery of Admissible Heuristics. Machine Learning 12, 165–175 (1995)
St-Aubin, R., Hoey, J., Boutilier, C.: APRICODD: Approximate Policy Construction Using Decision Diagrams. Neural Information Processing Systems 13 (2000)
Tash, J., Russell, S.: Control Strategies for a Stochastic Planner. In: Proc. of the Twelfth National Conference on Artificial Intelligence, pp. 1079–1085 (1994)
Valtorta, M.: A New Result on the Computational Complexity of Heuristic Estimates for the A* Algorithm. Artificial Intelligence 55(1), 129–142 (1992)
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Beliaeva, N., Zilberstein, S. (2005). Generating Admissible Heuristics by Abstraction for Search in Stochastic Domains. In: Zucker, JD., Saitta, L. (eds) Abstraction, Reformulation and Approximation. SARA 2005. Lecture Notes in Computer Science(), vol 3607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11527862_2
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DOI: https://doi.org/10.1007/11527862_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27872-6
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