  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.
