Distributed support-vector-machine over dynamic balanced directed networks

TL;DR

This paper introduces a hybrid continuous-time distributed SVM algorithm that adapts to dynamic directed networks, ensuring convergence without chattering by integrating network topology changes.

Contribution

It proposes a novel hybrid continuous-time algorithm for distributed SVMs that handles network topology changes and guarantees convergence on time-varying directed graphs.

Findings

Algorithm converges to the SVM classifier over time-varying graphs

Handles network topology changes with discrete jumps

Removes chattering caused by discretization

Abstract

In this paper, we consider the binary classification problem via distributed Support-Vector-Machines (SVM), where the idea is to train a network of agents, with limited share of data, to cooperatively learn the SVM classifier for the global database. Agents only share processed information regarding the classifier parameters and the gradient of the local loss functions instead of their raw data. In contrast to the existing work, we propose a continuous-time algorithm that incorporates network topology changes in discrete jumps. This hybrid nature allows us to remove chattering that arises because of the discretization of the underlying CT process. We show that the proposed algorithm converges to the SVM classifier over time-varying weight balanced directed graphs by using arguments from the matrix perturbation theory.