Learning Personalized Models with Clustered System Identification

System identification is the data-driven process of estimating a dynamic model of a system based on observations of the system trajectories. It plays a crucial role in aiding our understanding of complex systems and is a fundamental problem in numerous fields, including time-series analysis, control theory, robotics, and reinforcement learning (Åström and Eykhoff, 1971; Ljung, 1998). The effective utilization of available data is pivotal in obtaining an accurate model estimate with a measure of uncertainty quantification. Traditional system identification, methods (Ljung, 1998) have focused on asymptotic analysis, which, although insightful, is restrictive when dealing with small to medium sized data sets. Motivated by this, and the fact that data generation is often costly and time consuming, modern approaches focus on developing sample complexity bounds (i.e., non-asymptotic convergence analysis).