Iterative parameter mixing for distributed large-margin training of structured predictors for natural language processing
Coppola, Gregory Francis
The development of distributed training strategies for statistical prediction functions is important for applications of machine learning, generally, and the development of distributed structured prediction training strategies is important for natural language processing (NLP), in particular. With ever-growing data sets this is, first, because, it is easier to increase computational capacity by adding more processor nodes than it is to increase the power of individual processor nodes, and, second, because data sets are often collected and stored in different locations. Iterative parameter mixing (IPM) is a distributed training strategy in which each node in a network of processors optimizes a regularized average loss objective on its own subset of the total available training data, making stochastic (per-example) updates to its own estimate of the optimal weight vector, and communicating with the other nodes by periodically averaging estimates of the optimal vector across the network. This algorithm has been contrasted with a close relative, called here the single-mixture optimization algorithm, in which each node stochastically optimizes an average loss objective on its own subset of the training data, operating in isolation until convergence, at which point the average of the independently created estimates is returned. Recent empirical results have suggested that this IPM strategy produces better models than the single-mixture algorithm, and the results of this thesis add to this picture. The contributions of this thesis are as follows. The first contribution is to produce and analyze an algorithm for decentralized stochastic optimization of regularized average loss objective functions. This algorithm, which we call the distributed regularized dual averaging algorithm, improves over prior work on distributed dual averaging by providing a simpler algorithm (used in the rest of the thesis), better convergence bounds for the case of regularized average loss functions, and certain technical results that are used in the sequel. The central contribution of this thesis is to give an optimization-theoretic justification for the IPM algorithm. While past work has focused primarily on its empirical test-time performance, we give a novel perspective on this algorithm by showing that, in the context of the distributed dual averaging algorithm, IPM constitutes a convergent optimization algorithm for arbitrary convex functions, while the single-mixture distribution algorithm is not. Experiments indeed confirm that the superior test-time performance of models trained using IPM, compared to single-mixture, correlates with better optimization of the objective value on the training set, a fact not previously reported. Furthermore, our analysis of general non-smooth functions justifies the use of distributed large-margin (support vector machine [SVM]) training of structured predictors, which we show yields better test performance than the IPM perceptron algorithm, the only version of the IPM to have previously been given a theoretical justification. Our results confirm that IPM training can reach the same level of test performance as a sequentially trained model and can reach better accuracies when one has a fixed budget of training time. Finally, we use the reduction in training time that distributed training allows to experiment with adding higher-order dependency features to a state-of-the-art phrase-structure parsing model. We demonstrate that adding these features improves out-of-domain parsing results of even the strongest phrase-structure parsing models, yielding a new state-of-the-art for the popular train-test pairs considered. In addition, we show that a feature-bagging strategy, in which component models are trained separately and later combined, is sometimes necessary to avoid feature under-training and get the best performance out of large feature sets.
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