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.

该研究提出了一种从观察多种系统动态下的轨迹中学习线性系统模型的算法，其中系统根据相似性被分为不同的簇，并推导出一种通过估计系统簇身份并估计动态来更新每个簇模型的方法，从而实现更高效和个性化的系统识别过程。

利用集群系统识别学习个性化模型

Learning Personalized Models with Clustered System Identification

We study a collaborative scenario where a user not only instructs a system to
complete tasks, but also acts alongside it. This allows the user to adapt to
the system abilities by changing their language or deciding to simply
accomplish some tasks themselves, and requires the system to effectively
recover from errors as the user strategically assigns it new goals. We build a
game environment to study this scenario, and learn to map user instructions to
system actions. We introduce a learning approach focused on recovery from
cascading errors between instructions, and modeling methods to explicitly
reason about instructions with multiple goals. We evaluate with a new
evaluation protocol using recorded interactions and online games with human
users, and observe how users adapt to the system abilities.

我们研究了一种协作场景，其中用户不仅指示系统完成任务，而且与系统一起行动。我们通过建立一个游戏环境来研究这个场景，并学习将用户的指令映射到系统的动作，以实现误差恢复和多目标指令的显式推理。我们通过新的评估协议和人类用户的交互和在线游戏进行评估，并观察用户如何适应系统的能力。