The Stochastic Conjugate Subgradient Algorithm For Kernel Support Vector Machines

TL;DR

This paper introduces a stochastic conjugate subgradient algorithm tailored for kernel SVMs, offering faster convergence, better scalability, and improved accuracy over traditional stochastic first-order methods, especially in large-scale, non-smooth optimization problems.

Contribution

The paper presents a novel stochastic conjugate subgradient method with adaptive sampling and decomposition strategies for kernel SVMs, extending first-order methods to non-smooth, nonlinear problems.

Findings

Faster convergence per iteration compared to traditional SFO methods

Enhanced scalability in large-scale kernel SVM training

Improved speed and accuracy demonstrated in experiments

Abstract

Stochastic First-Order (SFO) methods have been a cornerstone in addressing a broad spectrum of modern machine learning (ML) challenges. However, their efficacy is increasingly questioned, especially in large-scale applications where empirical evidence indicates potential performance limitations. In response, this paper proposes an innovative method specifically designed for kernel support vector machines (SVMs). This method not only achieves faster convergence per iteration but also exhibits enhanced scalability when compared to conventional SFO techniques. Diverging from traditional sample average approximation strategies that typically frame kernel SVM as an 'all-in-one' Quadratic Program (QP), our approach adopts adaptive sampling. This strategy incrementally refines approximation accuracy on an 'as-needed' basis. Crucially, this approach also inspires a decomposition-based algorithm, effectively decomposing parameter selection from error estimation, with the latter being independently determined for each data point. To exploit the quadratic nature of the kernel matrix, we introduce a stochastic conjugate subgradient method. This method preserves many benefits of first-order approaches while adeptly handling both nonlinearity and non-smooth aspects of the SVM problem. Thus, it extends beyond the capabilities of standard SFO algorithms for non-smooth convex optimization. The convergence rate of this novel method is thoroughly analyzed within this paper. Our experimental results demonstrate that the proposed algorithm not only maintains but potentially exceeds the scalability of SFO methods. Moreover, it significantly enhances both speed and accuracy of the optimization process.