Years and Authors of Summarized Original Work
1994; Kearns, Valiant
Problem Definition
This entry deals with proving negative results for distribution-free PAC learning. The crux of the problem is proving that a polynomial-time algorithm for learning various concept classes in the PAC model implies that several well-known cryptosystems are insecure. Thus, if we assume a particular cryptosystem is secure, we can conclude that it is impossible to efficiently learn a corresponding set of concept classes.
PAC Learning
We recall here the PAC learning model. Let C be a concept class (a set of functions over n variables), and let D be a distribution over the input space {0, 1}n. With C we associate a size function size that measures the complexity of each c ∈ C. For example, if C is a class of Boolean circuits, then size(c) is equal to the number of gates in c. Let A be a randomized algorithm that has access to an oracle which returns labeled examples (x, c(x)) for some unknown c ∈ C; the...
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Alekhnovich M, Braverman M, Feldman V, Klivans AR, Pitassi T (2004) Learnability and automatizability. In: Proceedings of the 45th symposium on foundations of computer science, Rome
Angluin D, Kharitonov M (1995) When won’t membership queries help? J Comput Syst Sci 50(2):336-355
Goldreich O (2001) Foundations of cryptography: basic tools. Cambridge University Press, Cambridge/New York
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Kearns M, Vazirani U (1994) An introduction to computational learning theory. MIT, Cambridge
Kharitonov M (1993) Cryptographic hardness of distribution-specific learning. In: Proceedings of the twenty-fifth annual symposium on theory of computing, San Diego, pp 372–381
Klivans A, Sherstov AA (2006) Cryptographic hardness for learning intersections of halfspaces. In: Proceedings of the 47th symposium on foundations of computer science, Berkeley
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Valiant L (1984) A theory of the learnable. Commun ACM 27(11):1134–1142
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Klivans, A. (2016). Cryptographic Hardness of Learning. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_96
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