# A core-set approach for distributed quadratic programming in big-data classification

## TL;DR

This paper introduces a distributed algorithm for large-scale quadratic classification problems in cyber-physical networks, leveraging core-sets to efficiently approximate solutions in high-dimensional, big-data settings.

## Contribution

It presents a novel asynchronous distributed method that uses core-sets to handle high-dimensional, large-scale quadratic programming in networked systems.

## Key findings

- Algorithm scales with data size and dimension
- Achieves consensus on approximate solutions
- Effective in big-data classification tasks

## Abstract

A new challenge for learning algorithms in cyber-physical network systems is the distributed solution of big-data classification problems, i.e., problems in which both the number of training samples and their dimension is high. Motivated by several problem set-ups in Machine Learning, in this paper we consider a special class of quadratic optimization problems involving a "large" number of input data, whose dimension is "big". To solve these quadratic optimization problems over peer-to-peer networks, we propose an asynchronous, distributed algorithm that scales with both the number and the dimension of the input data (training samples in the classification problem). The proposed distributed optimization algorithm relies on the notion of "core-set" which is used in geometric optimization to approximate the value function associated to a given set of points with a smaller subset of points. By computing local core-sets on a smaller version of the global problem and exchanging them with neighbors, the nodes reach consensus on a set of active constraints representing an approximate solution for the global quadratic program.