MDL in the limit

Authors:
Pieter Adriaans;Wico Mulder
Affiliations:
University of Amsterdam, Amsterdam, The Netherlands;Logica, Amstelveen, The Netherlands
Venue:
ICGI'10 Proceedings of the 10th international colloquium conference on Grammatical inference: theoretical results and applications
Year:
2010

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Abstract

We show that within the Gold paradigm for language learning an informer for a superfinite set can cause an optimal MDL learner to make an infinite amount of mind changes. In this setting an optimal learner can make an infinite amount of wrong choices without approximating the right solution. This result helps us to understand the relation between MDL and identification in the limit in learning: MDL is an optimal model selection paradigm, identification in the limit defines recursion theoretical conditions for convergence of a learner.