Abstract
We address the problem of predicting the size of the search tree explored by Depth-First Branch and Bound (DFBnB) while solving optimization problems over graphical models. Building upon methodology introduced by Knuth and his student Chen, this paper presents a memory-efficient scheme called Retentive Stratified Sampling (RSS). Through empirical evaluation on probabilistic graphical models from various problem domains we show impressive prediction power that is far superior to recent competing schemes.
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References
Kask, K., Dechter, R.: A general scheme for automatic search heuristics from specification dependencies. Artificial Intelligence, 91–131 (2001)
Marinescu, R., Dechter, R.: Memory intensive AND/OR search for combinatorial optimization in graphical models. Artificial Intelligence 173, 1492–1524 (2009)
Otten, L., Dechter, R.: Anytime AND/OR depth first search for combinatorial optimization. In: Proceedings of the Symposium on Combinatorial Search, pp. 117–124. AAAI Press (2011)
de Givry, S., Schiex, T., Verfaillie, G.: Exploiting tree decomposition and soft local consistency in Weighted CSP. In: Proceedings of the AAAI Conference on Artificial Intelligence, pp. 22–27. AAAI Press (2006)
Balas, E., Toth, P.: Branch and bound methods. In: Lawler, E.L., Lenstra, J.K., Kart, A.H.G.R., Shmoys, D.B. (eds.) The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. John Wiley & Sons, New York (1985)
Otten, L., Dechter, R.: A case study in complexity estimation: Towards parallel branch-and-bound over graphical models. In: Proceedings of the Conference on Uncertainty in Artificial Intelligence, pp. 665–674 (2012)
Knuth, D.E.: Estimating the efficiency of backtrack programs. Math. Comp. 29, 121–136 (1975)
Chen, P.C.: Heuristic sampling: A method for predicting the performance of tree searching programs. SIAM Journal on Computing 21, 295–315 (1992)
Korf, R.E.: Depth-first iterative-deepening: An optimal admissible tree search. Artificial Intelligence 27, 97–109 (1985)
Purdom, P.W.: Tree size by partial backtracking. SIAM Journal of Computing 7, 481–491 (1978)
Korf, R.E., Reid, M., Edelkamp, S.: Time complexity of Iterative-Deepening-A*. Artificial Intelligence 129, 199–218 (2001)
Zahavi, U., Felner, A., Burch, N., Holte, R.C.: Predicting the performance of IDA* using conditional distributions. Journal of Artificial Intelligence Research 37, 41–83 (2010)
Burns, E., Ruml, W.: Iterative-deepening search with on-line tree size prediction. In: Proceedings of the International Conference on Learning and Intelligent Optimization, pp. 1–15 (2012)
Lelis, L.H.S.: Active stratified sampling with clustering-based type systems for predicting the search tree size of problems with real-valued heuristics. In: Proceedings of the Symposium on Combinatorial Search, pp. 123–131. AAAI Press (2013)
Lelis, L.H.S., Otten, L., Dechter, R.: Predicting the size of depth-first branch and bound search trees. In: International Joint Conference on Artificial Intelligence, pp. 594–600 (2013)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann (1988)
Dechter, R., Rish, I.: Mini-buckets: a general scheme for bounded inference. Journal of the ACM 50, 107–153 (2003)
Marinescu, R., Dechter, R.: AND/OR Branch-and-Bound search for combinatorial optimization in graphical models. Artificial Intelligence 173, 1457–1491 (2009)
Otten, L., Dechter, R.: Anytime AND/OR depth-first search for combinatorial optimization. AI Communications 25, 211–227 (2012)
Kilby, P., Slaney, J.K., Thiébaux, S., Walsh, T.: Estimating search tree size. In: Proceedings of the AAAI Conference on Artificial Intelligence, pp. 1014–1019. AAAI Press (2006)
Nilsson, N.: Principles of Artificial Intelligence. Morgan Kaufmann (1980)
Lelis, L.H.S., Zilles, S., Holte, R.C.: Predicting the Size of IDA*’s Search Tree. Artificial Intelligence, 53–76 (2013)
Dechter, R.: Reasoning with Probabilistic and Deterministic Graphical Models: Exact Algorithms. Synthesis Lectures on Artificial Intelligence and Machine Learning. Morgan & Claypool Publishers (2013)
Harvey, W.D., Ginsberg, M.L.: Limited discrepancy search. In: Proceedings of the International Joint Conference on Artificial Intelligence, pp. 607–613 (1995)
Xu, L., Hutter, F., Hoos, H.H., Leyton-Brown, K.: SATzilla: Portfolio-based Algorithm Selection for SAT. J. Artif. Intell. Res. (JAIR) 32, 565–606 (2008)
Leyton-Brown, K., Nudelman, E., Shoham, Y.: Empirical hardness models: Methodology and a case study on combinatorial auctions. Journal of the ACM 56, 1–52 (2009)
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Lelis, L.H.S., Otten, L., Dechter, R. (2014). Memory-Efficient Tree Size Prediction for Depth-First Search in Graphical Models. In: O’Sullivan, B. (eds) Principles and Practice of Constraint Programming. CP 2014. Lecture Notes in Computer Science, vol 8656. Springer, Cham. https://doi.org/10.1007/978-3-319-10428-7_36
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DOI: https://doi.org/10.1007/978-3-319-10428-7_36
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