Abstract
The question investigated in this paper is to what extent an input representation influences the success of learning, in particular from the point of view of analyzing agents that can interact with their environment. We investigate learning environments that have a group structure. We introduce a learning model in different variants and study under which circumstances group structures can be learned efficiently from experimenting with group generators (actions). Negative results are presented, even without efficiency constraints, for rather general classes of groups showing that even with group structure, learning an environment from partial information is far from trivial. However, positive results for special subclasses of Abelian groups turn out to be a good starting point for the design of efficient learning algorithms based on structured representations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Babai, L., Fried, K.: Approximate representation theory of finite groups. In: Proc. 32nd Annual Symposium on Foundations of Computer Science, pp. 733–742 (1991)
Babai, L., Szemerédi, E.: On the complexity of matrix group problems I. In: IEEE Symposium on Foundations of Computer Science (1984)
Boone, W.W.: The Word Problem. The Annals of Mathematics 70, 207–265 (1959)
Culberson, J.C., Schaeffer, J.: Pattern databases. Computational Intelligence 14, 318–334 (1998)
Friedl, K., Ivanyos, G., Santha, M.: Efficient testing of groups. In: Proc. 37th Annual ACM Symposium on Theory of Computing, pp. 157–166 (2005)
Gold, E.M.: Language identification in the limit. Inform. Control 10, 447–474 (1967)
Holte, R., Grajkowski, J., Tanner, B.: Hierarchical heuristic search revisited. In: Symposium on Abstraction, Reformulation and Approximation (2005)
Jaeger, H.: Observable operator models for discrete stochastic time series. Neural Computation 12, 1371–1398 (2000)
Korf, R.E.: Finding optimal solutions to Rubik’s cube using pattern databases. In: AAAI/IAAI, pp. 700–705 (1997)
Korf, R.E.: Analyzing the performance of pattern database heuristics. In: Proc. 22nd AAAI Conference on Artificial Intelligence, pp. 1164–1170 (2007)
Littman, M.L., Sutton, R., Singh, S.: Predictive representations of state. In: Advances in Neural Information Processing Systems 14, pp. 1555–1561 (2002)
Novikov, P.S.: On the algorithmic undecidability of the word problem in group theory. In: Proc. Steklov Institute of Mathematics, vol. 44, pp. 1–143 (1955) (in Russian)
Rivest, R.L., Schapire, R.E.: Diversity-based inference of finite automata. J. ACM, 555–589 (1994)
Rothman, J.J.: An Introduction to the Theory of Groups. Springer, Heidelberg (1995)
Stephan, F., Ventsov, Y.: Learning algebraic structures from text. Theoret. Comput. Sci. 268(2), 221–273 (2001)
Strehl, A.L., Diuk, C., Littman, M.L.: Efficient structure learning in factored-state MDPs. In: Proc. 22nd AAAI Conference on Artificial Intelligence, pp. 645–650 (2007)
Vinodchandran, N.V.: Counting Complexity and Computational Group Theory. PhD thesis, Institute of Mathematical Sciences, Chennai, India (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bartók, G., Szepesvári, C., Zilles, S. (2008). Active Learning of Group-Structured Environments. In: Freund, Y., Györfi, L., Turán, G., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 2008. Lecture Notes in Computer Science(), vol 5254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87987-9_28
Download citation
DOI: https://doi.org/10.1007/978-3-540-87987-9_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87986-2
Online ISBN: 978-3-540-87987-9
eBook Packages: Computer ScienceComputer Science (R0)