Teaching Memoryless Randomized Learners Without Feedback

  • Frank J. Balbach
  • Thomas Zeugmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4264)

Abstract

The present paper mainly studies the expected teaching time of memoryless randomized learners without feedback.

First, a characterization of optimal randomized learners is provided and, based on it, optimal teaching teaching times for certain classes are established. Second, the problem of determining the optimal teaching time is shown to be \({{\mathcal N\!P}}\)-hard. Third, an algorithm for approximating the optimal teaching time is given. Finally, two heuristics for teaching are studied, i.e., cyclic teachers and greedy teachers.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Angluin, D., Kriķis, M.: Teachers, learners and black boxes. In: Proc. 10th Ann. Conf. on Comput. Learning Theory, pp. 285–297. ACM Press, New York (1997)CrossRefGoogle Scholar
  2. 2.
    Angluin, D., Kriķis, M.: Learning from different teachers. Machine Learning 51(2), 137–163 (2003)MATHCrossRefGoogle Scholar
  3. 3.
    Anthony, M., Brightwell, G., Cohen, D., Shawe-Taylor, J.: On exact specification by examples. In: Proc. 5th Ann. ACM Works. on Comput. Learning Theory, pp. 311–318. ACM Press, New York (1992)CrossRefGoogle Scholar
  4. 4.
    Balbach, F.J.: Teaching Classes with High Teaching Dimension Using Few Examples. In: Auer, P., Meir, R. (eds.) COLT 2005. LNCS (LNAI), vol. 3559, pp. 668–683. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Balbach, F.J., Zeugmann, T.: Teaching randomized learners. In: Lugosi, G., Simon, H.U. (eds.) COLT 2006. LNCS (LNAI), vol. 4005, pp. 229–243. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Bertsekas, D.P.: Dynamic Programming and Optimal Control. Athena Sci. (2005)Google Scholar
  7. 7.
    Blondel, V.D., Canterini, V.: Undecidable problems for probabilistic automata of fixed dimension. Theory of Computing Systems 36(3), 231–245 (2003)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Freivalds, R., Kinber, E.B., Wiehagen, R.: On the power of inductive inference from good examples. Theoret. Comput. Sci. 110(1), 131–144 (1993)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, San Francisco (1979)MATHGoogle Scholar
  10. 10.
    Goldman, S.A., Kearns, M.J.: On the complexity of teaching. J. of Comput. Syst. Sci. 50(1), 20–31 (1995)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Goldman, S.A., Mathias, H.D.: Teaching a smarter learner. J. of Comput. Syst. Sci. 52(2), 255–267 (1996)CrossRefMathSciNetGoogle Scholar
  12. 12.
    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
  13. 13.
    Jackson, J., Tomkins, A.: A computational model of teaching. In: Proc. 5th Ann. ACM Works. on Comput. Learning Theory, pp. 319–326. ACM Press, New York (1992)CrossRefGoogle Scholar
  14. 14.
    Jain, S., Lange, S., Nessel, J.: On the learnability of recursively enumerable languages from good examples. Theoret. Comput. Sci. 261(1), 3–29 (2001)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Kuhlmann, C.: On Teaching and Learning Intersection-Closed Concept Classes. In: Fischer, P., Simon, H.U. (eds.) EuroCOLT 1999. LNCS (LNAI), vol. 1572, pp. 168–182. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  16. 16.
    Lee, H.K., Servedio, R.A., Wan, A.: DNF Are Teachable in the Average Case. In: Lugosi, G., Simon, H.U. (eds.) COLT 2006. LNCS (LNAI), vol. 4005, pp. 214–228. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  17. 17.
    Madani, O., Hanks, S., Condon, A.: On the undecidability of probabilistic planning and infinite-horizon partially observable markov decision problems. In: Proc. 16th Nat. Conf. on Artificial Intelligence & 11th Conf. on Innovative Applications of Artificial Intelligence, pp. 541–548. AAAI Press/MIT Press (1999)Google Scholar
  18. 18.
    Mathias, H.D.: A model of interactive teaching. J. of Comput. Syst. Sci. 54(3), 487–501 (1997)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Patek, S.D.: On partially observed stochastic shortest path problems. In: Proc. of the 40-th IEEE Conf. on Decision and Control, pp. 5050–5055 (2001)Google Scholar
  20. 20.
    Shinohara, A., Miyano, S.: Teachability in computational learning. New Generation Computing 8(4), 337–348 (1991)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

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

Personalised recommendations