# Learning Personalized Models with Clustered System Identification

arXiv: https://arxiv.org/abs/2304.01395 · HTML: https://mlsanity.com/paper/2304.01395/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 37 references that are in the map.
- First posted on arXiv 3 Apr 2023.

## Builds on (most cited first, 18 of 18)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)
- [An Efficient Framework for Clustered Federated Learning](https://mlsanity.com/paper/2006.04088/) (2020)
- [Clustered Federated Learning: Model-Agnostic Distributed Multi-Task Optimization under Privacy Constraints](https://mlsanity.com/paper/1910.01991/) (2019)
- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Statistical guarantees for the EM algorithm: From population to sample-based analysis](https://mlsanity.com/paper/1408.2156/) (2014)
- [Near optimal finite time identification of arbitrary linear dynamical systems](https://mlsanity.com/paper/1812.01251/) (2018)
- [Non-asymptotic Identification of LTI Systems from a Single Trajectory](https://mlsanity.com/paper/1806.05722/) (2018)
- [Learning Linear Dynamical Systems with Semi-Parametric Least Squares](https://mlsanity.com/paper/1902.00768/) (2019)
- [Non-asymptotic Identification of Linear Dynamical Systems Using Multiple Trajectories](https://mlsanity.com/paper/2009.00739/) (2020)
- [Multi-Task Imitation Learning for Linear Dynamical Systems](https://mlsanity.com/paper/2212.00186/) (2022)
- [FedSysID: A Federated Approach to Sample-Efficient System Identification](https://mlsanity.com/paper/2211.14393/) (2022)
- [Non-Asymptotic Analysis of Robust Control from Coarse-Grained Identification](https://mlsanity.com/paper/1707.04791/) (2017)
- [Identifying the Dynamics of a System by Leveraging Data from Similar Systems](https://mlsanity.com/paper/2204.05446/) (2022)
- [Multi-Task System Identification of Similar Linear Time-Invariant Dynamical Systems](https://mlsanity.com/paper/2301.01430/) (2023)
- [Learning Dynamical Systems by Leveraging Data from Similar Systems](https://mlsanity.com/paper/2302.04344/) (2023)
- [An Improved Algorithm for Clustered Federated Learning](https://mlsanity.com/paper/2210.11538/) (2022)

## Built on by (most cited first, 11 of 11)

- [Meta-Learning Linear Quadratic Regulators: A Policy Gradient MAML Approach for Model-free LQR](https://mlsanity.com/paper/2401.14534/) (2024)
- [Coreset-Based Task Selection for Sample-Efficient Meta-Reinforcement Learning](https://mlsanity.com/paper/2502.02332/) (2025)
- [Asynchronous Heterogeneous Linear Quadratic Regulator Design](https://mlsanity.com/paper/2404.09061/) (2024)
- [Expert with Clustering: Hierarchical Online Preference Learning Framework](https://mlsanity.com/paper/2401.15062/) (2024)
- [Combining Federated Learning and Control: A Survey](https://mlsanity.com/paper/2407.11069/) (2024)
- [Redefining Clustered Federated Learning for System Identification: The Path of ClusterCraft](https://mlsanity.com/paper/2505.16857/) (2025)
- [Adversarially Robust Multitask Adaptive Control](https://mlsanity.com/paper/2511.05444/) (2025)
- [Harnessing Data from Clustered LQR Systems: Personalized and Collaborative Policy Optimization](https://mlsanity.com/paper/2511.17489/) (2025)
- [The Nah Bandit: Modeling User Non-compliance in Recommendation Systems](https://mlsanity.com/paper/2408.07897/) (2024)
- [A State Alignment-Centric Approach to Federated System Identification: The FedAlign Framework](https://mlsanity.com/paper/2503.12137/) (2025)
- [Eigenspace-Based Clustering for Personalized System Identification](https://mlsanity.com/paper/2606.20811/) (2026)

## Abstract (arXiv)

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.