TY - GEN

T1 - Probabilistic generalization of simple grammars and its application to reinforcement learning

AU - Shibata, Takeshi

AU - Yoshinaka, Ryo

AU - Chikayama, Takashi

PY - 2006/1/1

Y1 - 2006/1/1

N2 - Recently, some non-regular subclasses of context-free grammars have been found to be efficiently learnable from positive data. In order to use these efficient algorithms to infer probabilistic languages, one must take into account not only equivalences between languages but also probabilistic generalities of grammars. The probabilistic generality of a grammar G is the class of the probabilistic languages generated by probabilistic grammars constructed on G. We introduce a subclass of simple grammars (SGs), referred as to unifiable simple grammars (USGs), which is a superclass of an efficiently learnable class, right-unique simple grammars (RSGs). We show that the class of RSGs is unifiable within the class of USGs, whereas SGs and RSGs are not unifiable within the class of SGs and RSGs, respectively. We also introduce simple context-free decision processes, which are a natural extension of finite Markov decision processes and intuitively may be thought of a Markov decision process with stacks. We propose a reinforcement learning method on simple context-free decision processes, as an application of the learning and unification algorithm for RSGs from positive data.

AB - Recently, some non-regular subclasses of context-free grammars have been found to be efficiently learnable from positive data. In order to use these efficient algorithms to infer probabilistic languages, one must take into account not only equivalences between languages but also probabilistic generalities of grammars. The probabilistic generality of a grammar G is the class of the probabilistic languages generated by probabilistic grammars constructed on G. We introduce a subclass of simple grammars (SGs), referred as to unifiable simple grammars (USGs), which is a superclass of an efficiently learnable class, right-unique simple grammars (RSGs). We show that the class of RSGs is unifiable within the class of USGs, whereas SGs and RSGs are not unifiable within the class of SGs and RSGs, respectively. We also introduce simple context-free decision processes, which are a natural extension of finite Markov decision processes and intuitively may be thought of a Markov decision process with stacks. We propose a reinforcement learning method on simple context-free decision processes, as an application of the learning and unification algorithm for RSGs from positive data.

UR - http://www.scopus.com/inward/record.url?scp=33750691692&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750691692&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33750691692

SN - 3540466495

SN - 9783540466499

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 348

EP - 362

BT - Algorithmic Learning Theory - 17th International Conference, ALT 2006, Proceedings

PB - Springer-Verlag

T2 - 17th International Conference on Algorithmic Learning Theory, ALT 2006

Y2 - 7 October 2006 through 10 October 2006

ER -