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We consider the class of optimization problems arising from computationallyintensive L1-regularized M-estimators, where the function or gradient valuesare very expensive to compute. A particular instance of interest is theL1-regularized MLE for learning Conditional Random Fields (CRFs), which are apopular class of statistical models for varied structured prediction problemssuch as sequence labeling, alignment, and classification with label taxonomy.L1-regularized MLEs for CRFs are particularly expensive to optimize sincecomputing the gradient values requires an expensive inference step. In thiswork, we propose the use of a carefully constructed proximal quasi-Newtonalgorithm for such computationally intensive M-estimation problems, where weemploy an aggressive active set selection technique. In a key contribution ofthe paper, we show that the proximal quasi-Newton method is provablysuper-linearly convergent, even in the absence of strong convexity, byleveraging a restricted variant of strong convexity. In our experiments, theproposed algorithm converges considerably faster than current state-of-the-arton the problems of sequence labeling and hierarchical classification.

Proximal Quasi-Newton for Computationally Intensive L1-regularized M-estimators