Naive Parameter Learning for Optimality Theory - The Hidden Structure Problem

There exist a number of provably correct learning algorithms for Optimality Theory and closely related theories. These include Constraint Demotion (CD; Tesar 1995, et seq.), a family of algorithms for classic OT. For Harmonic Grammar (Legendre, Miyata and Smolensky 1990; Smolensky and Legendre 2006) and related theories (e.g. maximum entropy), there is Stochastic Gradient Ascent (SGA; Soderstrom, Mathis and Smolensky 2006, Jäger 2007). There is also the Gradual Learning Algorithm for Stochastic OT (GLA; Boersma 1997), which works well in most cases but is known not to be correct in the general case (see e.g., Pater 2008). The success of these algorithms (and correctness proofs in the case of CD and SGA) relies on the assumption that learners are provided with full structural descriptions of the data, including prosodic structure as well as underlying representations, which are not available to the human learner.