Abstract
Algorithm selection, algorithm portfolios, and randomized restarts, can profit from a probabilistic model of algorithm run-time, to be estimated from data gathered by solving a set of experiments. Censored sampling offers a principled way of reducing this initial training time. We study the trade-off between training time and model precision by varying the censoring threshold, and analyzing the consequent impact on the performance of an optimal restart strategy, based on an estimated model of runtime distribution.
We present experiments with a SAT solver on a graph-coloring benchmark. Due to the “heavy-tailed” runtime distribution, a modest censoring can already reduce training time by a few orders of magnitudes. The nature of the optimization process underlying the restart strategy renders its performance surprisingly robust, also to more aggressive censoring.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Gomes, C.P., Fernandez, C., Selman, B., Bessiere, C.: Statistical regimes across constrainedness regions. Constraints 10(4), 317–337 (2005)
Rice, J.R.: The algorithm selection problem. In: Rubinoff, M., Yovits, M.C. (eds.) Advances in computers, vol. 15, pp. 65–118. Academic Press, New York (1976)
Hogg, T., Williams, C.P.: The hardest constraint problems: a double phase transition. Artif. Intell. 69(1-2), 359–377 (1994)
Gomes, C.P., Selman, B., Crato, N., Kautz, H.: Heavy-tailed phenomena in satisfiability and constraint satisfaction problems. J. Autom. Reason. 24(1-2), 67–100 (2000)
Huberman, B.A., Lukose, R.M., Hogg, T.: An economic approach to hard computational problems. Science 275, 51–54 (1997)
Luby, M., Sinclair, A., Zuckerman, D.: Optimal speedup of las vegas algorithms. Inf. Process. Lett. 47(4), 173–180 (1993)
Gomes, C.P., Selman, B.: Algorithm portfolios. Artificial Intelligence 126(1–2), 43–62 (2001)
Nelson, W.: Applied Life Data Analysis. John Wiley, New York (1982)
Li, C.M., Anbulagan: Heuristics based on unit propagation for satisfiability problems. In: IJCAI 1997, pp. 366–371 (1997)
Hoos, H.H., Stützle, T.: SATLIB: An Online Resource for Research on SAT. In: Gent, I.P., Maaren, H.v., Walsh, T. (eds.) SAT 2000, pp. 283–292. IOS Press, Amsterdam (2000), http://www.satlib.org
Frost, D., Rish, I., Vila, L.: Summarizing csp hardness with continuous probability distributions. In: AAAI/IAAI, pp. 327–333 (1997)
van Moorsel, A.P.A., Wolter, K.: Analysis and algorithms for restart. In: QEST 2004: Proceedings of the The Quantitative Evaluation of Systems, First International Conference on (QEST 2004), Washington, DC, USA, pp. 195–204. IEEE Computer Society, Los Alamitos (2004)
Hoos, H.H.: On the run-time behaviour of stochastic local search algorithms for sat. In: Proceedings of the Sixteenth National Conference on Artificial Intelligence (AAAI 1999), Orlando, Florida, pp. 661–666 (1999)
Hoos, H.H., Stützle, T.: Local search algorithms for SAT: An empirical evaluation. Journal of Automated Reasoning 24(4), 421–481 (2000)
Hoos, H.H.: A mixture-model for the behaviour of sls algorithms for sat. In: Eighteenth national conference on Artificial intelligence, pp. 661–667. American Association for Artificial Intelligence, Menlo Park (2002)
Boddy, M., Dean, T.L.: Deliberation scheduling for problem solving in time-constrained environments. Artificial Intelligence 67(2), 245–285 (1994)
Hansen, E.A., Zilberstein, S.: Monitoring and control of anytime algorithms: A dynamic programming approach. Artificial Intelligence 126(1–2), 139–157 (2001)
Alt, H., Guibas, L., Mehlhorn, K., Karp, R., Widgerson, A.: A method for obtaining randomized algorithms with small tail probalities. Research Report MPI-I-92-110, Max-Planck-Institut für Informatik, Im Stadtwald, D-66123 Saarbrücken, Germany (1992)
Gomes, C.P., Selman, B., Kautz, H.: Boosting combinatorial search through randomization. In: AAAI 1998/IAAI 1998: Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence, pp. 431–437. American Association for Artificial Intelligence, Menlo Park (1998)
Kautz, H., Horvitz, E., Ruan, Y., Gomes, C., Selman, B.: Dynamic restart policies (2002)
Gagliolo, M., Schmidhuber, J.: A neural network model for inter-problem adaptive online time allocation. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds.) ICANN 2005. LNCS, vol. 3697, pp. 7–12. Springer, Heidelberg (2005)
Gagliolo, M., Schmidhuber, J.: Dynamic algorithm portfolios. In: Ninth International Symposium on Artificial Intelligence and Mathematics, Fort Lauderdale, Florida (January 2006)
Gent, I., Hoos, H.H., Prosser, P., Walsh, T.: Morphing: Combining structure and randomness. In: Proc. of AAAI 1999, pp. 654–660 (1999), Benchmark avaliable at: http://www.intellektik.informatik.tu-darmstadt.de/SATLIB/Benchmarks/SAT/SW-GCP/descr.html
Reed, W.: The double pareto-lognormal distribution - a new parametric model for size distribution (2001), Available at: http://www.math.uvic.ca/faculty/reed/index.html
Kaplan, E.L., Meyer, P.: Nonparametric estimation from incomplete samples. J. of the ASA 73, 457–481 (1958)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gagliolo, M., Schmidhuber, J. (2006). Impact of Censored Sampling on the Performance of Restart Strategies. In: Benhamou, F. (eds) Principles and Practice of Constraint Programming - CP 2006. CP 2006. Lecture Notes in Computer Science, vol 4204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889205_14
Download citation
DOI: https://doi.org/10.1007/11889205_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46267-5
Online ISBN: 978-3-540-46268-2
eBook Packages: Computer ScienceComputer Science (R0)