Learning Personalized Models with Clustered System Identification
This work addresses collaborative system identification for multiple systems, offering incremental improvements in sample efficiency through clustering.
The paper tackles the problem of learning linear system models from multiple trajectories with different dynamics by clustering systems based on similarity, enabling systems within the same cluster to share observations. The result is an algorithm that correctly estimates cluster identities and achieves sample complexity scaling inversely with cluster size, improving efficiency and personalization.
We address the problem of learning linear system models from observing multiple trajectories from different system dynamics. This framework encompasses a collaborative scenario where several systems seeking to estimate their dynamics are partitioned into clusters according to their 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 approximate sample complexity that scales inversely with the number of systems in the cluster, thus facilitating a more efficient and personalized system identification process.