Abstract
Modeling a combinatorial problem is a hard and error-prone task requiring significant expertise. Constraint acquisition methods attempt to automate this process by learning constraints from examples of solutions and (usually) non-solutions. Active methods query an oracle while passive methods do not. We propose a known but not widely-used application of machine learning to constraint acquisition: training a classifier to discriminate between solutions and non-solutions, then deriving a constraint model from the trained classifier. We discuss a wide range of possible new acquisition methods with useful properties inherited from classifiers. We also show the potential of this approach using a Naive Bayes classifier, obtaining a new passive acquisition algorithm that is considerably faster than existing methods, scalable to large constraint sets, and robust under errors.
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Asdi, H.A., Bessiere, C., Ezzahir, R., Lazaar, N.: Time-bounded query generator for constraint acquisition. In: Proceedings of the 15th International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research, Lecture Notes in Computer Science, vol. 10848, pp 1–17 (2018)
Arcangioli, R., Bessiere, C., Lazaar, N.: Multiple constraint acquisition. In: Proceedings of the 25th International Joint Conference on Artificial Intelligence (2016)
Asafu-Adjei, J.K., Betensky, R.A.: A pairwise Naïve Bayes approach to Bayesian classification. Intern. J. Pattern Recognit. Artif. Intell. 29(7) (2015)
Bartolini, A., Lombardi, M., Milano, M., Benini, L.: Neuron constraints to model complex real-world problems. In: Proceedings of the 17th International Conference on Principles and Practice of Constraint Programming Lecture Notes in Computer Science, vol. 6876, pp 115–129 (2011)
Beldiceanu, N., Simonis, H.: Modelseeker: Extracting global constraint models from positive examples. In: Data Mining and Constraint Programming, Lecture Notes in Computer Science, vol. 10101, pp 77–95. Springer (2016)
Bessiere, C., Koriche, F., Lazaara, N., O’Sullivan, B.: Constraint acquisition. Artif. Intell. 244, 315–342 (2017)
Bessiere, C., Coletta, R., Freuder, E.C., O’Sullivan, B.: Leveraging the learning power of examples in automated constraint acquisition. In: Proceedings of the 10th International Conference on Principles and Practice of Constraint Programming Lecture Notes in Computer Science, vol. 3258, pp 123–137 (2004)
Bessiere, C., Coletta, R., Daoudi, A., Lazaar, N., Bouyakhf, E.H.: Boosting constraint acquisition via generalization queries. In: Proceedings of the 21st European Conference on Artificial Intelligence, pp 99–104 (2014)
Bessiere, C., Coletta, R., Hebrard, E., Katsirelos, G., Lazaar, N., Narodytska, N., Quimper, C.-G., Walsh, T.: Constraint acquisition via partial queries. In: Proceedings of the 23rd International Joint Conference on Artificial Intelligence, pp 475–481. AAAI Press (2013)
Bonfietti, A., Lombardi, M., Milano, M.: Embedding decision trees and random forests in constraint programming. In: Proceedings of the International Conference on AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, Lecture Notes in Computer Science, vol. 9075, pp 74–90. Springer (2015)
Browne, D., Giering, M., Prestwich, S.D.: Pulse-net: Dynamic compression of convolutional neural networks. In: Proceedings of the IEEE 5th World Forum on Internet of Things (2019)
Casale, P., Pujol, O., Radeva, P.: Approximate convex hulls family for One-Class classification. In: proceedings of the International Workshop on Multiple Classifier Systems Lecture in Notes Computer Sci, vol. 6713, pp 106–115 (2011)
Cheng, B.M.W., Choi, K.M.F., Lee, H.H.M., Wu, J.C.K.: Increasing constraint propagation by redundant modeling: An experience report. Constraints 4, 167–192 (1999)
Domingos, P., Pazzani, M.: On the optimality of the simple bayesian classifier under Zero-One loss. Mach. Learn. 29, 103–130 (1997)
Fischetti, M., Jo, J.: Deep neural networks as 0-1 mixed integer linear programs: A feasibility study. Constraints 23(3), 296–309 (2018)
Frankle, J., Carbin, M.: The lottery ticket hypothesis: Finding sparse, trainable neural networks. In: Proceedings of the International Conference on Learning Representations. to appear (2019)
Freuder, E.C.: Constraints: The ties that bind. In: Proceedings of the 21st National Conference on Artificial Intelligence, pp 1520–1523. AAAI Press (2006)
Freuder, E.C.: Progress towards the holy grail. Constraints 23, 158–171 (2018)
Freuder, E.C., Wallace, R.J.: Suggestion strategies for Constraint-Based matchmaker agents. Int. J. Artif. Intell. Tools 11(1), 3–18 (2002)
Gent, I.P., Petrie, K.E., Puget, J.-F.: Handbook of Constraint Programming. Elsevier, Amsterdam (2006)
Good, I.J.: Turing’s anticipation of empirical Bayes in connection with the cryptanalysis of the naval enigma. J. Stat. Comput. Simul. 66(2), 101–111 (2000)
Hnich, B., Prestwich, S.D., Selensky, E., Smith, B.M.: Constraint models for the covering test problem. Constraints 11(3), 199–219 (2006)
Kass, R.E., Raftery, A.E.: Bayes Factors. J. Amer. Stat. Assoc. 90(430), 773–795 (1995)
Khan, S., Madden, M.: One-Class Classification: Taxonomy of study and review of techniques. Knowl. Eng. Rev. 29(3), 345–374 (2014)
Kolb, S., Paramonov, S., Guns, T., De Raedt, L.: Learning constraints in spreadsheets and tabular data. Mach. Learn. 106, 1441–1468 (2017)
Lallouet, A., Lopez, M., Martin, L., Vrain, C.: On learning constraint problems. In: Proceedings of the IEEE International Conference on Tools With Artificial Intelligence, pp 45–52 (2010)
Lallouet, A., Legtchenko, A.: Two contributions of constraint programming to machine learning. In: Proceedings of the European Conference on Machine Learning Lecture Notes in Artificial Intelligence, vol. 3720, pp 617–624. Springer (2005)
Lombardi, M., Milano, M.: Boosting combinatorial problem modeling with machine learning. In: Proceedings of the 27th International Joint Conference on Artificial Intelligence, pp 5472–5478 (2018)
Lombardi, M., Milano, M., Bartolini, A.: Empirical decision model learning. Artif. Intell. 244(Supplement C), 343–367 (2017)
Manning, C.D., Raghavan, P., Schütze, M.: Introduction to information retrieval. Cambridge University Press, Cambridge (2008)
Prestwich, S.D.: Robust constraint acquisition by sequential analysis. In: Proceedings of the 24th European Conference on Artificial Intelligence, Frontiers in Artificial Intelligence and Applications, vol. 325, pp 355–362. IOS Press (2020)
O’Sullivan, B.: Automated modelling and solving in constraint programming. In: Proceedings of the 24th AAAI Conference on Artificial Intelligence, pp 1493–1497 (2010)
Pawlak, T.P., Krawiec, K.: Automatic synthesis of constraints from examples using mixed integer linear programming. Eur. J. Oper. Res. 261(3), 1141–1157 (2017)
De Raedt, L., Dehaspe, L.: Clausal discovery. Mach. Learn. 26, 99–146 (1997)
De Raedt, L., Dz̆eroski, S.: First Order jk-clausal Theories are PAC-learnable. Artif. Intell. 70, 375–392 (1994)
De Raedt, L., Passerini, A., Reso, S.: Learning constraints from examples. In: Proceedings of the 32nd AAAI Conference on Artificial Intelligence, pp 7965–7970 (2018)
Say, B., Wu, G., Zhou, Y.Q., Sanner, S.: Nonlinear hybrid planning with deep net learned transition models and mixed-integer linear programs. In: Proceedings of the 26th International Joint Conference on Artificial Intelligence, pp 750–756 (2017)
Smith, B.M., Stergiou, K., Walsh, T.: Modelling the Golomb Ruler Problem. In: Proceedings of the 16th International Joint Conference on Artificial Intelligence (1999)
Snell, J., Swersky, K., Zemel, R.: Prototypical networks for few-shot learning. In: Proceedings of the 31st Conference on Neural Information Processing Systems (2017)
Tjeng, V., Tedrake, R.: Verifying neural networks with mixed integer programming. coRR (2017)
Tseitin, G.: On the complexity of derivation in propositional calculus. In: Siekmann, J., Wrightson, G. (eds.) Automation of Reasoning: Classical Papers in Computational Logic, vol. 2, pp 466–483. Springer (1983)
Tsouros, D.C., Stergiou, K., Sarigiannidis, P.G.: Efficient methods for constraint acquisition. In: Proceedings of the 24th International Conference on Principles and Practice of Constraint Programming, Lecture Notes in Computer Science, vol. 11008, pp 373–388 (2018)
Tsouros, D.C., Stergiou, K., Bessiere, C.: Structure-driven multiple constraint acquisition. In: 25th International Conference on Principles and Practice of Constraint Programming Lecture Notes in Computer Science, vol. 11802, pp 709–725 (2019)
Valiant, L.G.: A theory of the learnable. Commun. ACM 27(11), 1134–1142 (1984)
Verwer, S., Zhang, Y., Ye, Q.C.: Auction optimization using regression trees and linear models as integer programs. Artif. Intell. 244, 368–395 (2017)
Vinyals, O., Blundell, C., Lillicrap, T., Kavukcuoglu, K., Wierstra, D.: Matching networks for one shot learning. In: Proceedings of the 30th Conference on Neural Information Processing Systems, pp 3637–3645 (2016)
Vu, X.-H., O’Sullivan, B.: A unifying framework for generalized constraint acquisition. Int. J. Artif. Intell. Tools 17(5), 803–833 (2008)
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This material is based upon works supported by the Science Foundation Ireland under Grant No. 12/RC/2289-P2 which is co-funded under the European Regional Development Fund.
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Prestwich, S.D., Freuder, E.C., O’Sullivan, B. et al. Classifier-based constraint acquisition. Ann Math Artif Intell 89, 655–674 (2021). https://doi.org/10.1007/s10472-021-09736-4
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DOI: https://doi.org/10.1007/s10472-021-09736-4