While the covariance-based policy parameterization offers advantages such as efficient use of data and recursive updates, it also has potential limitations compared to other data-driven LQR formulations. One limitation is the assumption of linearity in the system dynamics, which may restrict the applicability of the method to linear systems only. Nonlinear systems may not be accurately represented by the covariance-based parameterization, leading to suboptimal control performance. Additionally, the dimensionality of the covariance matrix can grow with the size of the data, potentially increasing computational complexity and memory requirements. This scalability issue may limit the method's efficiency for large-scale systems or long-term data collection scenarios.