| Summary: | Online semi-supervised learning (OS<sup>2</sup>L) has received much attention recently because of its well practical usefulness. Most of the existing studies of OS<sup>2</sup>L are related to manifold regularization. In this paper, we introduce a novel OS<sup>2</sup>L framework with multiple regularization terms based on the notion of ascending the dual function in constrained optimization. Using the Fenchel conjugate, different semi-supervised regularization terms can be integrated into the dual function easily and directly. This approach is derived by updating limited dual coefficient variables on each learning round. To be practical, we also employ buffering strategies and sparse approximation approaches in this paper. The experimental studies show that our methods achieve accuracy comparable to offline algorithms while consuming less time and memory. Especially, our OS<sup>2</sup>L algorithms can handle the settings where the target hyperplane of classification continually drifts with the sequence of arriving instances. This paper paves a way to design and analyze OS<sup>2</sup>L algorithms with multiple regularization terms.
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