Primal-Dual Gradient Flow Algorithm for Distributed Support Vector Machines

TL;DR

This paper introduces a primal-dual gradient flow algorithm for distributed support vector machines, enabling a network of nodes with partitioned data to asymptotically reach the optimal solution through passivity and Lyapunov stability analysis.

Contribution

It proposes a novel primal-dual gradient flow method for DSVM that guarantees convergence using passivity and Lyapunov functions.

Findings

Nodes are passive dynamical systems.

Algorithm ensures asymptotic convergence to optimal solution.

The method is suitable for distributed large-scale datasets.

Abstract

In this paper, a primal-dual gradient flow algorithm for distributed support vector machines (DSVM) is proposed. A network of computing nodes, each carrying a subset of horizontally partitioned large dataset is considered. The nodes are represented as dynamical systems with Arrow-Hurwicz-Uzawa gradient flow dynamics, derived from the Lagrangian function of the DSVM problem. It is first proved that the nodes are passive dynamical systems. Then, by employing the Krasovskii type candidate Lyapunov functions, it is proved that the computing nodes asymptotically converge to the optimal primal-dual solution.