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Generalized Discriminative Feature Transformation (GDFT) is a feature space discriminative training algorithm for automatic speech recognition (ASR). GDFT uses Lagrange relaxation to transform the constrained maximum likelihood linear regression (CMLLR) algorithm for feature space discriminative training. This paper presents recent improvements on GDFT, which are achieved by regularization to the optimization problem. The resulting algorithm is called regularized GDFT (rGDFT) and we show that many regularization and smoothing techniques developed for model space discriminative training are also applicable to feature space training. We evaluated rGDFT on a real-time Iraqi ASR system and also on a large scale Arabic ASR task.