Kernel-based online learning has often shown state-of-the-art performance for
many online learning tasks. It, however, suffers from a major shortcoming, that
is, the unbounded number of support vectors, making it non-scalable and
unsuitable for applications with large-scale datasets. In this work, we study
the problem of bounded kernel-based online learning that aims to constrain the
number of support vectors by a predefined budget. Although several algorithms
have been proposed in literature, they are neither computationally efficient
due to their intensive budget maintenance strategy nor effective due to the use
of simple Perceptron algorithm. To overcome these limitations, we propose a
framework for bounded kernel-based online learning based on an online gradient
descent approach. We propose two efficient algorithms of bounded online
gradient descent (BOGD) for scalable kernel-based online learning: (i) BOGD by
maintaining support vectors using uniform sampling, and (ii) BOGD++ by
maintaining support vectors using non-uniform sampling. We present theoretical
analysis of regret bound for both algorithms, and found promising empirical
performance in terms of both efficacy and efficiency by comparing them to
several well-known algorithms for bounded kernel-based online learning on
large-scale datasets.Comment: ICML201
