Stochastic gradient descent (SGD) uses approximate gradients estimated from subsets of the training data and updates the parameters in an online fashion. This learning framework is attractive because it often requires much less training time in practice than batch training algorithms. However, Ll-regularization, which is becoming popular in natural language processing because of its ability to produce compact models, cannot be efficiently applied in SGD training, due to the large dimensions of feature vectors and the fluctuations of approximate gradients. We present a simple method to solve these problems by penalizing the weights according to cumulative values for L1 penalty. We evaluate the effectiveness of our method in three applications: text chunking, named entity recognition, and part-of-speech tagging. Experimental results demonstrate that our method can produce compact and accurate models much more quickly than a state-of-the-art quasi-Newton method for Ll-regularized log-linear models.
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