Communication-Efficient Parallel Block Minimization for Kernel Machines

TL;DR

This paper introduces a communication-efficient parallel block minimization framework for kernel machines, significantly accelerating large-scale kernel SVM and logistic regression training on distributed systems.

Contribution

The paper proposes a novel parallel block minimization method with a communication-efficient line search, enabling faster training of kernel machines on large datasets.

Findings

Achieves 96% accuracy in 20 seconds on covtype dataset with 32 machines.

Outperforms existing parallel solvers by reducing training time from over 2000 seconds to 20 seconds.

Scales to datasets with 8 million samples and 20 million features.

Abstract

Kernel machines often yield superior predictive performance on various tasks; however, they suffer from severe computational challenges. In this paper, we show how to overcome the important challenge of speeding up kernel machines. In particular, we develop a parallel block minimization framework for solving kernel machines, including kernel SVM and kernel logistic regression. Our framework proceeds by dividing the problem into smaller subproblems by forming a block-diagonal approximation of the Hessian matrix. The subproblems are then solved approximately in parallel. After that, a communication efficient line search procedure is developed to ensure sufficient reduction of the objective function value at each iteration. We prove global linear convergence rate of the proposed method with a wide class of subproblem solvers, and our analysis covers strongly convex and some non-strongly convex functions. We apply our algorithm to solve large-scale kernel SVM problems on distributed systems, and show a significant improvement over existing parallel solvers. As an example, on the covtype dataset with half-a-million samples, our algorithm can obtain an approximate solution with 96% accuracy in 20 seconds using 32 machines, while all the other parallel kernel SVM solvers require more than 2000 seconds to achieve a solution with 95% accuracy. Moreover, our algorithm can scale to very large data sets, such as the kdd algebra dataset with 8 million samples and 20 million features.