A simplex Armijo downhill algorithm for optimizing statistical machine translation decoding parameters

We propose a variation of simplex-downhill algorithm specifically customized for optimizing parameters in statistical machine translation (SMT) decoder for better end-user automatic evaluation metric scores for translations, such as versions of BLEU, TER and mixtures of them. Traditional simplex-downhill has the advantage of derivative-free computations of objective functions, yet still gives satisfactory searching directions in most scenarios. This is suitable for optimizing translation metrics as they are not differentiable in nature. On the other hand, Armijo algorithm usually performs line search efficiently given a searching direction. It is a deep hidden fact that an efficient line search method will change the iterations of simplex, and hence the searching trajectories. We propose to embed the Armijo inexact line search within the simplex-downhill algorithm. We show, in our experiments, the proposed algorithm improves over the widely-applied Minimum Error Rate training algorithm for optimizing machine translation parameters.