We consider sequential maximization of performance metrics that are general functions of a confusion matrix of a classifier (such as precision, F-measure, or G-mean). Such metrics are, in general, non-decomposable over individual instances, making their optimization very challenging. While they have been extensively studied under different frameworks in the batch setting, their analysis in the online learning regime is very limited, with only a few distinguished exceptions. In this paper, we introduce and analyze a general online algorithm that can be used in a straightforward way with a variety of complex performance metrics in binary, multi-class, and multi-label classification problems. The algorithm's update and prediction rules are appealingly simple and computationally efficient without the need to store any past data. We show the algorithm attains $\mathcal{O}(\frac{\ln n}{n})$ regret for concave and smooth metrics and verify the efficiency of the proposed algorithm in empirical studies.

Topic models are popular for modeling discrete data (e.g., texts, images, videos, links), and provide an efficient way to discover hidden structures/semantics in massive data. One of the core problems in this field is the posterior inference for individual data instances. This problem is particularly important in streaming environments, but is often intractable. In this paper, we investigate the use of the Frank-Wolfe algorithm (FW) for recovering sparse solutions to posterior inference. From detailed elucidation of both theoretical and practical aspects, FW exhibits many interesting properties which are beneficial to topic modeling. We then employ FW to design fast methods, including ML-FW, for learning latent Dirichlet allocation (LDA) at large scales. Extensive experiments show that to reach the same predictiveness level, ML-FW can perform tens to thousand times faster than existing state-of-the-art methods for learning LDA from massive/streaming data.