Prior Knowledge in Learning Finite Parameter Spaces

We propose a new framework for computational analysis of language acquisition in a finite parameter space, for instance, in the "principles and parameters" approach to language. The prior knowledge multi-armed bandit algorithm abstracts the idea of a casino of slot machines in which a player has to play machines in order to find out how good they are, but where he has some prior knowledge that some machines are likely to have similar rates of reward. Each grammar is represented as an arm of a bandit machine with the mean-reward function drawn from a Gaussian Process specified by a covariance function between grammars. We test our algorithm on a ten-parameter space and show that the number of iterations required to identify the target grammar is much smaller than the number of all the possible grammars that the learner would have to explore if he was searching exhaustively the entire parameter space.