Results on memory-limited U-shaped learning

  • Authors:

  • Lorenzo Carlucci;John Case;Sanjay Jain;Frank Stephan

  • Affiliations:

  • University of Roma “La Sapienza”, Department of Computer Science, Via Salaria 113, 00198 Roma, Italy and Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126, Pisa, Italy;Department of Computer and Information Sciences, University of Delaware, Newark, DE 19716-2586, USA;School of Computing, National University of Singapore, Singapore 117543, Republic of Singapore;School of Computing and Department of Mathematics, National University of Singapore, Singapore 117543, Republic of Singapore

  • Venue:
  • Information and Computation
  • Year:
  • 2007

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Abstract

U-shaped learning is a learning behaviour in which the learner first learns a given target behaviour, then unlearns it and finally relearns it. Such a behaviour, observed by psychologists, for example, in the learning of past-tenses of English verbs, has been widely discussed among psychologists and cognitive scientists as a fundamental example of the non-monotonicity of learning. Previous theory literature has studied whether or not U-shaped learning, in the context of Gold's formal model of learning languages from positive data, is necessary for learning some tasks. It is clear that human learning involves memory limitations. In the present paper we consider, then, the question of the necessity of U-shaped learning for some learning models featuring memory limitations. Our results show that the question of the necessity of U-shaped learning in this memory-limited setting depends on delicate tradeoffs between the learner's ability to remember its own previous conjecture, to store some values in its long-term memory, to make queries about whether or not items occur in previously seen data and on the learner's choice of hypotheses space.