Part of the Lecture Notes in Computer Science book series (LNCS, volume 9206)
Alchemist: Learning Guarded Affine Functions
We present a technique and an accompanying tool that learns guarded affine functions. In our setting, a teacher starts with a guarded affine function and the learner learns this function using equivalence queries only. In each round, the teacher examines the current hypothesis of the learner and gives a counter-example in terms of an input-output pair where the hypothesis differs from the target function. The learner uses these input-output pairs to learn the guarded affine expression. This problem is relevant in synthesis domains where we are trying to synthesize guarded affine functions that have particular properties, provided we can build a teacher who can answer using such counter-examples. We implement our approach and show that our learner is effective in learning guarded affine expressions, and more effective than general-purpose synthesis techniques.
KeywordsTarget Function Numerical Attribute Affine Function Linear Expression Leaf Plane
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
We thank Sariel Har-Peled for discussions on geometric techniques for synthesizing leaf expressions. This work was partially supported by NSF Expeditions in Computing ExCAPE Award #1138994.
- 1.Alur, R., Bodík, R., Juniwal, G., Martin, M.M.K., Raghothaman, M., Seshia, S.A., Singh, R., Solar-Lezama, A., Torlak, E., Udupa, A.: Syntax-guided synthesis. In: Formal Methods in Computer-Aided Design, FMCAD 2013, Portland, OR, USA, 20–23 October 2013, pp. 1–17 (2013)Google Scholar
- 2.Alur, R., Singhania, N.: Precise piecewise affine models from input-output data. In: Proceedings of the 14th International Conference on Embedded Software, EMSOFT 2014, pp. 3:1–3:10. ACM, New York, NY, USA (2014)Google Scholar
- 3.Angluin, D.: Queries and concept learning. Mach. Learn. 2(4), 319–342 (1988)Google Scholar
- 8.Quinlan, J.R.: Induction of decision trees. Mach. Learn. 1(1), 81–106 (1986)Google Scholar
- 9.Quinlan, J.R.: C4.5: Programs for Machine Learning. Morgan Kaufmann, San Francisco (1993)Google Scholar
- 11.Solar-Lezama, A., Tancau, L., Bodík, R., Seshia, S.A., Saraswat, V.A.: Combinatorial sketching for finite programs. In: Proceedings of the 12th International Conference on Architectural Support for Programming Languages and Operating Systems, ASPLOS 2006, San Jose, CA, USA, 21–25 October 2006, pp. 404–415 (2006)Google Scholar
- 12.Vidal, R., Soatto, S., Sastry, S.: An algebraic geometric approach to the identification of a class of linear hybrid systems. In: Proceedings of the IEEE Conference on Decision and Control, vol. 1, pp. 167–172, December 2003Google Scholar
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