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The pairwise objective paradigms are an important and essential aspect ofmachine learning. Examples of machine learning approaches that use pairwiseobjective functions include differential network in face recognition, metriclearning, bipartite learning, multiple kernel learning, and maximizing of areaunder the curve (AUC). Compared to pointwise learning, pairwise learning'ssample size grows quadratically with the number of samples and thus itscomplexity. Researchers mostly address this challenge by utilizing an onlinelearning system. Recent research has, however, offered adaptive sample sizetraining for smooth loss functions as a better strategy in terms of convergenceand complexity, but without a comprehensive theoretical study. In a distinctline of research, importance sampling has sparked a considerable amount ofinterest in finite pointwise-sum minimization. This is because of thestochastic gradient variance, which causes the convergence to be slowedconsiderably. In this paper, we combine adaptive sample size and importancesampling techniques for pairwise learning, with convergence guarantees fornonsmooth convex pairwise loss functions. In particular, the model is trainedstochastically using an expanded training set for a predefined number ofiterations derived from the stability bounds. In addition, we demonstrate thatsampling opposite instances at each iteration reduces the variance of thegradient, hence accelerating convergence. Experiments on a broad variety ofdatasets in AUC maximization confirm the theoretical results.

Pairwise Learning via Stagewise Training in Proximal Setting