Convergence of Error-driven Ranking Algorithms

According to the OT error-driven ranking model of language acquisition, the learner performs a sequence of slight re-rankings triggered by mistakes on the incoming stream of data, until it converges to a ranking that makes no more mistakes. This learning model is very popular in the OT acquisition literature, in particular because it predicts a sequence of rankings that models gradualness in child acquisition. Two implementations of this learning model have been developed in the OT computational literature, namely Tesar and Smolensky’s (1998) Error-Driven Constraint Demotion (EDCD) and Boersma’s (1997) Gradual Learning Algorithm (GLA). Yet, EDCD only performs constraint demotion, and it is thus shown to predict a ranking dynamics too simple from a modeling perspective. The GLA performs both constraint demotion and promotion, but has been shown not to converge. This paper thus develops a complete theory of convergence of error-driven ranking algorithms that perform both constraint demotion and promotion. In particular, it shows that convergent constraint promotion can be achieved (with an error-bound that compares well to that of EDCD) through a proper calibration of the amount by which constraints are promoted.