Teaching Learners with Restricted Mind Changes

  • Frank J. Balbach
  • Thomas Zeugmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3734)

Abstract

Within learning theory teaching has been studied in various ways. In a common variant the teacher has to teach all learners that are restricted to output only consistent hypotheses. The complexity of teaching is then measured by the maximum number of mistakes a consistent learner can make until successful learning. This is equivalent to the so-called teaching dimension. However, many interesting concept classes have an exponential teaching dimension and it is only meaningful to consider the teachability of finite concept classes.

A refined approach of teaching is proposed by introducing a neighborhood relation over all possible hypotheses. The learners are then restricted to choose a new hypothesis from the neighborhood of their current one. Teachers are either required to teach finitely or in the limit. Moreover, the variant that the teacher receives the current hypothesis of the learner as feedback is considered.

The new models are compared to existing ones and to one another in dependence of the neighborhood relations given. In particular, it is shown that feedback can be very helpful. Moreover, within the new model one can also study the teachability of infinite concept classes with potentially infinite concepts such as languages. Finally, it is shown that in our model teachability and learnability can be rather different.

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References

  1. 1.
    Angluin, D.: Queries and concept learning. Machine Learning 2(4), 319–342 (1988)Google Scholar
  2. 2.
    Angluin, D.: Queries revisited. In: Abe, N., Khardon, R., Zeugmann, T. (eds.) ALT 2001. LNCS (LNAI), vol. 2225, pp. 12–31. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Angluin, D., Kriķis, M.: Teachers, learners and black boxes. In: Proc. 10th Annual Conference on Computational Learning Theory, pp. 285–297. ACM Press, New York (1997)CrossRefGoogle Scholar
  4. 4.
    Angluin, D., Kriķis, M.: Learning from different teachers. Machine Learning 51(2), 137–163 (2003)MATHCrossRefGoogle Scholar
  5. 5.
    Anthony, M., Brightwell, G., Cohen, D., Shawe-Taylor, J.: On exact specification by examples. In: Proc. 5th Annual ACM Workshop on Computational Learning Theory, pp. 311–318. ACM Press, New York (1992)CrossRefGoogle Scholar
  6. 6.
    Balbach, F.J., Zeugmann, T.: Teaching Learners that can only Perform Restricted Mind Changes, TCS Technical Report, Series A, TCS-TR-A-05-5, Division of Computer Science, Hokkaido University, July 18 (2005)Google Scholar
  7. 7.
    Ben-David, S., Eiron, N.: Self-directed learning and its relation to the VC-di- mension and to teacher-directed learning. Machine Learning 33(1), 87–104 (1998)MATHCrossRefGoogle Scholar
  8. 8.
    Freivalds, R., Kinber, E.B., Wiehagen, R.: Learning from good examples. In: Lange, S., Jantke, K.P. (eds.) GOSLER 1994. LNCS (LNAI), vol. 961, pp. 49–62. Springer, Heidelberg (1995)Google Scholar
  9. 9.
    Goldman, S.A., Kearns, M.J.: On the complexity of teaching. J. of Comput. Syst. Sci. 50(1), 20–31 (1995)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Goldman, S.A., Mathias, H.D.: Teaching a smarter learner. J. of Comput. Syst. Sci. 52(2), 255–267 (1996)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Goldman, S.A., Rivest, R.L., Schapire, R.E.: Learning binary relations and total orders. SIAM J. Comput. 22(5), 1006–1034 (1993)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Goldman, S.A., Sloan, R.H.: The power of self-directed learning. Machine Learning 14(3), 271–294 (1994)Google Scholar
  13. 13.
    Jackson, J., Tomkins, A.: A computational model of teaching. In: Proc. 5th Annual ACM Workshop on Computational Learning Theory, pp. 319–326. ACM Press, New York (1992)CrossRefGoogle Scholar
  14. 14.
    Jain, S., Lange, S., Nessel, J.: Learning of r.e. languages from good examples. In: Li, M. (ed.) ALT 1997. LNCS (LNAI), vol. 1316, pp. 32–47. Springer, Heidelberg (1997)Google Scholar
  15. 15.
    Mathias, H.D.: A model of interactive teaching. J. of Comput. Syst. Sci. 54(3), 487–501 (1997)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Rivest, R.L., Yin, Y.L.: Being taught can be faster than asking questions. In: Proc. 8th Annual Conference on Computational Learning Theory, pp. 144–151. ACM Press, New York (1995)CrossRefGoogle Scholar
  17. 17.
    Shinohara, A., Miyano, S.: Teachability in computational learning. New Generation Computing 8(4), 337–348 (1991)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Frank J. Balbach
    • 1
  • Thomas Zeugmann
    • 2
  1. 1.Institut für Theoretische InformatikUniversität zu LübeckLübeckGermany
  2. 2.Division of Computer ScienceHokkaido UniversitySapporoJapan

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