Fast Bounded Online Gradient Descent Algorithms for Scalable Kernel-Based Online Learning

TL;DR

This paper introduces two efficient bounded online gradient descent algorithms for scalable kernel-based online learning, effectively limiting support vectors and improving computational efficiency on large datasets.

Contribution

The paper proposes a novel framework with two algorithms, BOGD and BOGD++, that enhance scalability and efficiency in bounded kernel-based online learning.

Findings

Both algorithms achieve favorable regret bounds.

Empirical results show improved efficiency and effectiveness.

Algorithms outperform existing methods on large-scale datasets.

Abstract

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.