Learning attribute-efficiently with corrupt oracles

We study learning in a modified EXACT model, where the oracles are corrupt and only few of the presented attributes are relevant. Both modifications were already studied in the literature [Dana Angluin, Mārtiņš Krikis, Learning with malicious membership queries and exceptions (extended abstract), in: COLT ’94: Proceedings of the Seventh Annual Conference on Computational Learning Theory, ACM Press, 1994, pp. 56–57 [3]; Dana Angluin, Mārtiņš Krikis, Robert H. Sloan, György Turán, Malicious omissions and errors in answers to membership queries, Machine Learning 28 (1997) 211–255; Laurence Bisht, Nader H. Bshouty, Lawrance Khoury, Learning with errors in answers to membership queries (extracted abstract), in: FOCS ’04: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, FOCS’04, IEEE Computer Society, 2004, pp. 611–620; Nader H. Bshouty, Lisa Hellerstein, Attribute-efficient learning in query and mistake-bound models, J. Comput. System Sci. 56 (3) (1998) 310–319 [12]; Nick Littlestone, Learning quickly when irrelevant attributes abound: A new linear-threshold algorithm, Machine Learning 2 (4) (1988) 285–318; Robert H. Sloan, Gyorgy Turan, Learning with queries but incomplete information (extended abstract), in: COLT ’94: Proceedings of the Seventh Annual Conference on Computational Learning Theory, ACM Press, 1994, pp. 237–245 [5]], and efficient solutions were found to most of their variants. Nonetheless, their reasonable combination is yet to be studied, and integrating the existing solutions either fails or works with a complexity that can be significantly improved. In this paper we prove the equivalence of EXACT learning attribute-efficiently with and without corrupt oracles. For each of the possible scenarios we describe a generic scheme that enables learning in these cases using modifications of the standard learning algorithms. We also generalize and improve previous non-attribute-efficient algorithms for learning with corrupt oracles.