Learning Personalized Models with Clustered System Identification

We address the problem of learning linear system models by observing multiple trajectories from systems with differing dynamics. This framework encompasses a collaborative scenario where several systems seeking to estimate their dynamics are partitioned into clusters according to system similarity. Thus, the systems within the same cluster can benefit from the observations made by the others. Considering this framework, we present an algorithm where each system alternately estimates its cluster identity and performs an estimation of its dynamics. This is then aggregated to update the model of each cluster. We show that under mild assumptions, our algorithm correctly estimates the cluster identities and achieves an
$\varepsilon$
-approximate solution with a sample complexity that scales inversely with the number of systems in the cluster, thus facilitating a more efficient and personalized system identification.